Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

Tutors Answer Your Questions about Functions (FREE)

Question 571300: What is the domain of y=x^3-4
Answer by lwsshak3(2915)

You can put this solution on YOUR website!
What is the domain of y=x^3-4
If you do not see any denominators or square roots in the expression, there are no restrictions and the domain is: all real numbers or (-∞,∞)

Question 571211: A little help and understanding with this one is greatly appreciated...
Find f(x) and g(x) such that h(x) = (f o g)(x).
h(x) = |6x + 9|

Answer by richard1234(4789)

(Show Source):

You can put this solution on YOUR website!
Let
f(x) = |x|
g(x) = 6x+9
Then,
f(g(x)) = |6x+9|

Question 571210: The point (6,-3) is on the graph of y=f(x). Find the corresponding point on the graph of g(x)=f(3x)
Big troubles on this one for some reason...any help is greatly appreciated.
Answer by richard1234(4789)

(Show Source):

You can put this solution on YOUR website!
All we know is f(6) = -3 and g(x) = f(3x). The only point on g(x) that we can find occurs when x = 2. This is because g(2) = f(3*2) = f(6) (in other words, I basically set 3x = 6). Since we know f(6) = -3, g(2) must also be -3, so (2,-3) is the corresponding point.

Question 571128: I have to determine whether the graphs of each pair of lines are parallel...Please help.
Answer by KMST(578)

(Show Source):

You can put this solution on YOUR website!
To find, without graphing, if the graphs of two linear equations are parallel, look at the slopes. If the slopes are the same number, the lines are parallel or the equations could represent the same line. (If the slopes are different, the lines would intersect at just one common point, and if the product of the slopes is -1, the lines are perpendicular).
To find the slope, you could solve for y to get the slope-intercept form of the equation.
For example, 3x-2y=5

can be solved for y
3x-2y=5

-->

-->

-->

-->

-->

-->

, which is the slope-intercept form of the equation.
The coefficient of x in the slope-intercept form of the equation is the slope. (The independent term, or constant,-5/2 in this case, is the intercept or y-intercept).
Finding the slope-intercept form of 3x-2y=5

tells you that its graph is parallel to the graph of y=%283%2F2%29x%2B4

and that the graph of 3x-2y=5

is the same line as the graph of y=%283%2F2%29x-5%2F2

. It also tells you that the graph of 3x-2y=5

is not parallel to the graph of any other line that does not have 3/2 as its slope.
Beware of linear equations like y=%283%2F2%29%28x-1%29-1

because as you simplify it
y=%283%2F2%29%28x-1%29-1

-->

-->

-->

you realize that its graph is not a line parallel to the graph of y=%283%2F2%29x-5%2F2

. It is the same line.
Solving for y and getting the slope from the slope-intercept form of the equation will give you the answer in all cases, except if there is no y in your equation(s). A linear equation with only x and no y, like x=4

, represents a vertical line, which has no slope (its slope is said to be undefined). A vertical line can only be parallel to another vertical line.
NOTE:
In some case, you may not need to solve for y.
For example,
3x-2y=5

and

, where the same x-y expression is stated as equal to two different numbers, are parallel. You can see that for the same value of y, x must be 1 more for 3x-2y=8

, so its graph is like the other one, but moved 1 unit to the right.

Question 571039: If f(x)= x^2 + 3, g(x)=4x, the value of g(f(6)) is ?
Found 2 solutions by richard1234, nyc_function:
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
g(f(6)) means "g of f(6)," so find f(6).

f(6) = 6^2 + 3 = 39

So g(f(6)) = g(39) = 4*39 = 156

Answer by nyc_function(2626)   (Show Source):
You can put this solution on YOUR website!
First find f(6).
f(6) = (6)^2 + 3

f(6) = 36 + 3

f(6) = 39

Now plug 39 into g(x).

g(x) = 4x

g(f(6)) = 4x

g(39) = 4(39)

The answer is 156.

Question 571130: Sorry I forgot to write out the pair of lines
3x+8=y
2y=6x-3
are these lines parallel?
Found 2 solutions by Maths68, mananth:
Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!
3x+8=y............(1)
y=3x+8
Compare above equation with the standard equation of the line
y=mx+b
slope =m=3 and y-intercept =b=8
2y=6x-3...........(2)
Divide above equation by 2
2y/2=(6x-3)/2
y=6x/2-3/2
y=3x-3/2
Compare above equation with the standard equation of the line
y=mx+b
slope =m=3 and y-intercept =b=-3/2

Both lines are parallel because their slopes are same.

Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
3x+8=y
y=3x+8

2y=6x-3
/2
y=3x-(3/2)
compare both the lines with y= mx+b
m the slope of both lines are 3 so the lines are parallel

Question 570877: Please help me solve this equation
Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation
------

Multiply by 2x
1 + 6x = 0
6x = -1
x = -1/6

Question 570769: find the domain of function :
f(x)= √(15-3x )
what is the domain of f?
Answer by KMST(578)   (Show Source):
You can put this solution on YOUR website!
If , the value of the function will only exist if
--> --> or
The domain is restricted to real numbers not greater than 5.

Question 570711: Can you solve this by graphing?
y=-3x+3
6x+y=6
The solution set is what? Type an ordered pair ( )

Thank you!
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
-3 x +1 y = -3................(1)
6 x 1 y = 6.....................2)
equation1 3 = 3
when x= 0, y= 3, ( 0 , 3 )
when y = 0, x= 1, ( 1 , 0 )
Equation 2
when x= 0, y= 6, ( 0 , 6 )
when y = 0, x= 1, ( 1 , 0 )

Solution (1,0)

Question 570532: Rosa works due north of home. Her husband Ray works due east. They leave for work at the same time. By the time Rosa is 5 miles from home the distance between them is one mile more than Ray's distance from home. How far from home is Ray?
Answer by Earlsdon(6098)   (Show Source):
You can put this solution on YOUR website!
You can form a right triangle of this situation with Rosa's distance from home (5 miles) as the height and Ray's distance from home as the base (call it x miles). The distance between them is represented by the hypotenuse of the right triangle (call this x+1 miles).
Invoking the Pythagorean theorem () where: , , and we'll solve for x:

Subtract from both sides.
Subtract 1 from both sides.
Divide by 2.

Ray is 12 miles fom home.

Question 570371: Determine whether the function has an inverse function, and if so, find the inverse: QUOTE
The number N of bacteria in a refrigerated food is given by
where T is the temperature of the food (in degrees Celsius). When the food is removed from refrigeration, the temperature of the food is given by: QUOTE

where t is the time (in hours).
Find the composition N(T(t)) and interpret its meaning in context.
Find the number of bacteria in the food when t = 2 hours.
Find the time when the bacteria count reaches 2000.
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
Equation missing from post

Question 570165: what is the slope of a binomial (-2,4) (-4-4)

Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
what is the slope of a binomial (-2,4) (-4-4)
--------------
A binomial doesn't have a slope.
There's no binomial shown.
------
The slope of the line passing thru those 2 points is
m = diffy/diffx = (-8)/-2)
m = 4

Question 570062: Find (g of f)(x) and domain of (g of f)
f(x)=4x+5
g(x)= 2/x
(g of f)(x)= Simplified answer...
Domain of (g of f)...
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
Find (g of f)(x) and domain of (g of f)
f(x)=4x+5
g(x)= 2/x
--------------------
g[f(x)] = g[4x+5] = 2/(4x+5)
---------------
The denominator cannot be zero.
Domain: All Real Numbers except x = -5/4
==============================================
Cheers,
Stan H.
==============

Question 569869: Can this be solved... 21 square root of 35 over 7 square root of 5?
Thank you. How did you do it?
Thanks again.
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
21 square root of 35 over 7 square root of 5
-----
(21sqrt(35))/(7sqrt(5))
-----
= (3sqrt(7))
==================
cheers,
Stan H.
========

Question 569874: What is the value of B in the equation A = (h/2)(B+b)
Answer by nerdybill(5404)   (Show Source):
You can put this solution on YOUR website!
A = (h/2)(B+b)
2A = h(B+b)
2A/h = B+b
2A/h - b = B

Question 569622: how do i graph constant function of f(x)=2 and use the graph to identify domain and range of f

Answer by JBarnum(1826)   (Show Source):
You can put this solution on YOUR website!
y is always at 2 so no matter what x you have y will stay at 2
1,2
2,2
3,2
4,2
its a horizontal line at (0,2)
domain is what the x's are and range is what the y's are
y is always 2 so the range = {2}
x can be any numer negative or possitive so domain ={-infinity,infinity}

Question 569216: Find ƒ(–5) for each function.
ƒ(x) = 5x + 35
ƒ(x) = 5x + 35
Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
Find ƒ(–5) for each function.
ƒ(x) = 5x + 35
Sub 5 for x
f(5) = 5*5 + 35 = 25 + 35
f(5) = 60
---------------
ƒ(x) = 5x + 35
That looks familiar.

Question 568736: what's the domain of the function:
x^2-4/x-2
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
You cannot divide by zero. So x-2 cannot be zero. This means that the domain is the set of all real numbers except x cannot be 2 (since that makes x-2 equal to zero)

Question 568654: What is the domain of SQRT((x+5)/(x^2-25))
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
What is the domain of SQRT((x+5)/(x^2-25))
----------
The denominator cannot be zero,
so x cannot be +5 or -5
------
The radicand cannot be negative;
solve (x+5)/[(x+5)(x-5)] >= 0
-------
Draw a number line:
Plot x = -5 and x = 5
---
Test values to find the solutions:
Let x = -10 ; you get -/(-*-) > 0 ; false
-------
Let x = 0 ; you get +/(+*-) > 0 ; false
-------
Let x = 10; you get +/(+*+) > 0 ; true
==========================================
Domain: x > 5
====================
Cheers,
Stan H.
=================

Question 568572: 23>-x/2-5
Found 2 solutions by lwsshak3, jim_thompson5910:
Answer by lwsshak3(2915)   (Show Source):
You can put this solution on YOUR website!
23>-x/2-5
multiply by -2 and reverse inequality sign
-46 -56 x>-56
solution in interval notation:
(-56,∞)

Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
23>-x/2-5

23+5>-x/2

28 > -x/2

28*(-2) < x

-56 < x

x > -56
-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

Question 568557: Hi,
could you please tell me how I would go about finding the solution to this problem:
if
f(2) = 3 and f(6) = 5, then what is f(10) ?
Thank you very much!
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
I'm assuming that this is a linear function. If f(2) = 3 and f(6) = 5, then the line has the points (2, 3) and (6, 5). So let's find the equation of the line that goes through these points.

First let's find the slope of the line through the points and

Note: is the first point . So this means that and .
Also, is the second point . So this means that and .

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points and is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 3 to both sides.

Combine like terms.

So the equation that goes through the points and is

Therefore, the function is

Which means that

-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

Question 568532: Which of the following is NOT included in the domain of f(x)=6x+2 divided by x square-9? a.3 b.-3,3 c.9 d.-3
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Since you CANNOT divide by zero, this means that x^2-9 cannot be zero. Notice how x=-3 and x=3 make x^2-9 zero. So they are NOT in the domain.

So the answer is choice B
-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

Question 568415: Hi, I'm taking an online math class as a freshman in high school and I'm making a 65 because I can't figure out how to work the problems can you help me by explaining how to do this problem with all the steps
if h(x)=3x+2 and g(x)=f(x)-2, then what does g(3)=
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
g(x)=f(x)-2

g(3)=f(3)-2

The only problem is that we have no idea what the function f(x) is, so we cannot go any further. Make sure that there are no typos.

Question 568428: What is the value of f(-3). The equation is f(-3)?f(x) = 2x second power+ 5x-9
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Start with the given function

Plug in (ie replace every x with -3)

Square -3 to get 9

Multiply

Combine like terms

So the answer is
-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

Question 568191: What is the domain for d(x)=x+3
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
The domain is the set of all real numbers since you can plug in any number in for x (and get some number as the output).

Question 567954: Solve the following function.Show all work
24^x=1
Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
x=0
-----
24^x=1
x*log(24) = 0
x = 0

Question 567928: the value of y varies with x and y=12 when x=-6 find y when x=-4
Answer by Horlaye(3)   (Show Source):
You can put this solution on YOUR website!
Y varies as x
y=kx ( where k is the constant )
then we subtitute for the values of y and x to know the value of our constant.
12=-6k, divide both sides by the co-efficient of k
therefore k=-2
(y=-2x) :the law of variation.
Hence find y when x=-4
y=-2x
y=-2(-4)
y=8

Question 567789: The following function is one to one find its inverse.Find the domain and range of
f and f^-1
f(x)=3x+1/4
Answer by lwsshak3(2915)   (Show Source):
You can put this solution on YOUR website!
The following function is one to one find its inverse.Find the domain and range of
f and f^-1
f(x)=3x+1/4
**
y=3x+1/4
To find the inverse, interchange x and y, then solve for y.
x=3y+1/4
3y=x-1/4
y=x/3-1/12
f^-1=x/3-1/12
..
Both f and f^-1 are equations for straight lines which mean there are no restrictions, that is,
domain and range for both are all real numbers or (-∞,∞) in interval notation.

Question 567578: 10x/2+1 =64 find the value of x
Answer by MNSue(6)   (Show Source):
You can put this solution on YOUR website!
x = 63/5 or 12 3/5

Question 567523: I am taking an algebra class involving functions. I can not find what "choose an integer close to the origin" means. It says to choose any value to substitute for x, but the ones I choose turns out wrong, how do I choose the right values? Thankyou in advance.
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
The origin is the point (0,0) on an xy-coordinate plane. So choose integer values like 0, -1, 1, etc.

Question 567442: Find the x-intercept and y-intercept of the line given by the equation.
7x-7y+6=0

Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
7x-7y+6=0
7x-7y=-6

Find the Y & X intercepts of the two lines by plugging x=0, & y=0
equation
when x= 0,y=0.86(0, 6/7 )
when y =0,x=-0.86(-6/7 ,0)

Question 567296: x+5/x^2-36
find the domain
Answer by nerdybill(5404)   (Show Source):
You can put this solution on YOUR website!

The "domain" specifies all valid values of x.
In this case, if the denominator is zero, the expression is undefined.
This means that x can take be any value EXCEPT when:
x^2-36 = 0
x^2 = 36
x = +-6
.
Therefore the domain is:
(-oo, -6) U (-6, 6) U (6, +oo)
where
oo represents infinity

Question 567258: state the domain of the given function!y=3x-5/x+4
Answer by nyc_function(2626)   (Show Source):
You can put this solution on YOUR website!
The domain is going to be all the values for x that can be allowed that will not create division by zero. As you know, we cannot divide by zero.
Set denominator to zero and solve for x.

x + 4 = 0
x = -4
DOMAIN = ALL real numbers except x CANNOT = 0.

Question 566526: I have no idea how to solve this problem and i need help.
f(6)=2/6-2
Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!
Equation is not clearly written
However, if it is as follows

Take LCD

Or
If equation is as follows

Question 566339: How do you solve this problem step by step 2(x-y)=8 where x=6
Answer by Tias_411(14)   (Show Source):
You can put this solution on YOUR website!
substitute the 6 in for x.. this makes into . now use distributive property and multiply your 2 by everything in (). then subtract 12 from both sides of the equation (12-2y) -12 and 8-12. giving you then divide by -2... y = 2

Question 566302: Let f(x) = 3x + 2 and g(x) = 7x + 6.
Find (f • g) and its domain.
Answer by ad_alta(170)   (Show Source):
You can put this solution on YOUR website!
Simply "plug" g into f. We get (f • g)=3(7x+6)+2=21x+20. There aren't any numbers you can't plug into this function, so the domain is all reals.

Question 566214: find the domain of the function algebraically h(x)=√(9-x²)
Answer by lwsshak3(2915)   (Show Source):
You can put this solution on YOUR website!
find the domain of the function algebraically h(x)=√(9-x²)
Domain of radicans≥0
9-x^2≥0
(3+x)(3-x)≥0
number line
<..+...-3...-....3....+....>
Domain:
(-∞,-3] U [3,∞)

Question 565931: give an example of three f,g, and h (none of which is a constant function) such that fog=foh, but g is not equal to h.
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
Let

f(x) = x^2
g(x) = x
h(x) = -x

Then f(g(x)) = x^2 and f(h(x)) = (-x)^2 = x^2.

Question 565454: HOW DO YOU DETERMINE THE TURNING POINTS OF A GRAPH GIVEN THE FUNCTION: F(X)=2(X-3)(X^2+4)^3

Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
Take the derivative of f with respect to x (I used the product rule):

Set it equal to zero and find all real x that satisfy. Once you have done this, check to make sure that the sign of f'(x) actually changes.

Question 565905: What is the domain of f(x)= x^2 - 5x + 7 and of its derivative f '(x)=2x - 5? and then compare both domains.
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
What is the domain of f(x)= x^2 - 5x + 7 and of its derivative f '(x)=2x - 5? and then compare both domains.
----
Both have All Real Numbers as their domain.
Cheers,
Stan H.

Question 565316: Reading "50 Mathematical Ideas you really need to know". It gives Galileo's distance formula - y = 16 times x squared. It says the factor 16 is because feet and seconds are the chosen measurement units. Don't understand why 16? This is the introduction to Calculus and I haven't got past this number 16 yet.
Thank you, Chris.
Answer by Theo(2967)   (Show Source):
You can put this solution on YOUR website!
the formula is 16 * x^2 because the measurement was done in feet and seconds.
if the measurement was done in some other measure, like inches in half a second intervals, the factors would have been different.
the more generalized formula would be:
d = k * x^2 where:
k is the distance the object falls in 1 unit of time.
x is the unit of time.
for example:
assume the distance was in inches and the time in seconds.
the formula would then have become:
d = (16*12 = 192) * x^2 where:
192 is the distance in inches and x is the number of seconds.
assume the distance was in feet and the time interval was half a second.
the formula would then have become:
d = 4 * x^2 where:
4 is the number of feet the object fell in half a second and x is the number of half seconds.
the formula works the same either way.
the following chart should demonstrate that.
a is from the equation d = 16 * x^2 where 16 is the the number of feet in 1 second and x is the number of seconds.
b is from the equation d = 192 * x^2 where 192 is the number of inches in 1 second and x is the number of seconds.
c is from the equation d = 4 * x^2 where 4 is the number of feet in half a second and x is the number of half seconds.

seconds half seconds a b c 1 2 16 192 16 2 4 64 768 64 3 6 144 1728 144 15 30 3600 43200 3600

note that the results are the same regardless of the units used as long as you did the conversions correctly.
3600 feet * 12 inches per foot equals 43200 inches.
16 * 15^2 = 3600
4 * 30^2 = 3600
the formula is valid regardless of the units used.
the reason why the formula you are looking at is d = 16 * x^2 where 16 is the number of feet it dropped in 1 second and x is the number of seconds is because those are the units of measure that were used in galileo's observation.
from what i read, he may have actually used meters.
the formula would have been d = 4.9 * x^2 where 4.9 is the number of meters in 1 second.
4.9 meters is roughly equivalent to 16 feet which is why you see 16 feet.

Question 565181: what is the domain of h(x)=-6x^2/(x-1)(x+5)
Answer by ad_alta(170)   (Show Source):
You can put this solution on YOUR website!
You can put any real number you want into h(x), except 1 and -5. These points require the function to divide by zero and are therefore not in the domain.