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Tutors Answer Your Questions about Functions (FREE)
Question 758959: Find the domain:
f(x)=3x^(2)+1 Answer by jim_thompson5910(28715) (Show Source):
Question 759031: Please help me with this equation a graphing relation
x = 1 -y^2 Answer by MathLover1(6812) (Show Source):
You can put this solution on YOUR website!
make a table, choose several values for  coordinate, find  coordinate, plot all points and draw a line through
 |
 |  ........  =>  =>
 |  ........  =>  =>
 |  ........  =>  =>
 |  ........  =>  =>  complex root (as you can see, domain is all  ; so, you can continue to use only negative numbers
 |  ........  =>  =>
 |  ........  =>  =>
Question 759006: How do you find the graph of C(x)=(2x+5)/(x+1) Answer by Alan3354(31528) (Show Source):
You can put this solution on YOUR website!How do you find the graph of C(x)=(2x+5)/(x+1)
----------------
You'll probably have to make it. You could search for it for a long time.
Question 758847: Please help me solve this problem:
-3< 2x-1/5 < 0
This sign -> / means 2x-1 is over 5, as a fraction. < 0 is not a part of the fraction Answer by stanbon(57967) (Show Source):
Question 758848: Solve -1<2-x<4 Answer by stanbon(57967) (Show Source):
Question 758845: Please help me solve |3x|+4< 34 Answer by stanbon(57967) (Show Source):
Question 758743: What is the domain of this function: g(t)=9/sqrt5t+20 ? Answer by tommyt3rd(1112) (Show Source):
You can put this solution on YOUR website!Placement of parentheses affects the meaning of what we write. Assuming you wrote exactly what you meant which was:
t can be any number except 0
if this is not what you meant then please repost with a clear and complete question
Question 758410: If f(x)=x^2+1, find f(a+1) Found 2 solutions by stanbon, jim_thompson5910: Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!If f(x)=x^2+1, find f(a+1)
-----
f(a+1) = (a+1)^2 + 1 = a^2 + 2a + 2
==============================
Cheers,
Stan H.
===============
Answer by jim_thompson5910(28715) (Show Source):
You can put this solution on YOUR website!f(x)=x^2+1
f(a+1)=(a+1)^2+1 ... replace ALL copies of 'x' with 'a+1'
f(a+1)=(a+1)(a+1)+1
f(a+1)=a(a+1)+1(a+1)+1
f(a+1)=a^2+a+a+1+1
f(a+1)=a^2+2a+2
So the answer is f(a+1)=a^2+2a+2
Question 758349: Please help me:
Given functions f(x) = 3x and g(x) =x-5, find (f of g)(x) Answer by tommyt3rd(1112) (Show Source):
Question 758289: Please help me solve this equation:
If f(x) = x^2 - 2x + 3, find f(x + 2) Answer by nerdybill(7008) (Show Source):
You can put this solution on YOUR website!f(x) = x^2 - 2x + 3
.
f(x+2) = (x+2)^2 -2(x+2) +3
f(x+2) = (x+2)(x+2) -2(x+2) +3
f(x+2) = x^2+4x+4 -2(x+2) +3
f(x+2) = x^2+4x+4 -2x-2 +3
f(x+2) = x^2+2x+4-2 +3
f(x+2) = x^2+2x+2 +3
f(x+2) = x^2+2x+5
Question 758239: The range of the function f: N→N defined by f(x)= (-1)^x-1 Answer by tommyt3rd(1112) (Show Source):
Question 758242: The range of the function f: N→N defined by f(x)= (-1)^x-1 Found 2 solutions by tommyt3rd, stanbon: Answer by tommyt3rd(1112) (Show Source): Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!The range of the function f: N→N defined by f(x)= (-1)^(x-1)
----
(-1)^(even natural number) = 1
------------
(-1)^(odd natural number) = -1
----
Range = {-1,1}
====================
Cheers,
Stan H.
====================
Question 758126: given that f(x)=2x+1/3x+4 determine f^1(x)
Answer by nerdybill(7008) (Show Source):
You can put this solution on YOUR website!given that f(x)=2x+1/3x+4 determine f^1(x)
.
I'll assume you meant:
f(x)=(2x+1)/(3x+4)
.
replace f(x) with y:
y=(2x+1)/(3x+4)
switch variables:
x = (2y+1)/(3y+4)
multiplying both sides by (3y+4):
x(3y+4) = (2y+1)
3xy+4x = 2y+1
3xy = 2y+1-4x
3xy-2y = 1-4x
y(3x-2) = 1-4x
y = (1-4x)/(3x-2)
.
So,
f^1(x) = (1-4x)/(3x-2)
Question 757974: What is the value of f(x)=36^x when x=1/2?
A. 3
B. 6
C. 18
D. 72
Please Explain!!! Answer by Alan3354(31528) (Show Source):
Question 757855: Which point belongs to -y2 = x?
Is it: a. ( 2,1 ) b. ( 4,-2 ) c. ( -4, -2 ) d. ( 4, 2 ) and what would be the solution?
Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!Which point belongs to -y2 = x?
Is it:
a. ( 2,1)::::::-(1)^2 = 2::::: No
----------------------------------
b. ( 4,-2 ):::: -(-2)^2 = 4:::: No
---------------------------------
c. ( -4, -2)::: -(-2)^2 = -4::: Yes
-----------------------------------
d. ( 4, 2 ):::: -(2)^2 = 4::::: No
and what would be the solution?
y = -2 when x = -4
========================
cheers,
Stan H.
===============
Question 757725: Find the function value:
find f(-11) when f(x)= -5x-14
Please show steps as I am really confused with this. Thanks. Answer by jim_thompson5910(28715) (Show Source):
You can put this solution on YOUR website!f(x)= -5x-14
f(-11)= -5(-11)-14 ... plug in x = -11 (ie replace EVERY x with -11). Now evaluate/simplify
f(-11)= 55-14
f(-11)= 41
So the final answer is f(-11)= 41
Question 757684: Find the domain of the composite function f*g
f(x)=4/x-2;g(x)=9/x
The domain ____
Answer by josgarithmetic(1774) (Show Source):
You can put this solution on YOUR website!You indicate the multiplication or product of the two functions.

=
The only restriction is that  .
The domain is the real numbers  and  .
Question 757668: Solve the exponential equation. Express the solution in terms of natural logarithms. Use calculator to obtain a decimal approximation for the solution.
e^x=13.7
What is the solution in terms of natural logorithms?
Solution set___ Answer by Alan3354(31528) (Show Source):
Question 757529: Would you please help me to answer this:
Find the LCD of both fractions, then simplify the expression. Assume that no denominator equals zero.
5/(3x^2y) - 4/(6xy^3)
Thanks
Found 2 solutions by Cromlix, sachi: Answer by Cromlix(733) (Show Source):
You can put this solution on YOUR website!5/(3x^2y) - 4/(6xy^3)
LCD = 6x^2y^3
3x^2y divides into 6x^2y^3
giving 2y^2 to multiply
5 = 10y^2
6xy^3 divides into 6x^2y^3
giving x to multiply
4 = 4x
= 10y^2 - 4x/ 6x^2y^3
Hope this helps.
:-)
Answer by sachi(463) (Show Source):
Question 757527: Could you please help me to solve this:
Simplify the expression:
(x^2+3x+2)/(x+2)
Thanks Answer by sachi(463) (Show Source):
Question 757410: find the domain of (f + g)(x)when f(x) =2x+5and g (x)=4/x-2 Answer by josgarithmetic(1774) (Show Source):
You can put this solution on YOUR website!Not know exactly what you mean for g(x), but if you mean this:
 when  and
The the composition you indicate is 2x+5+(4/x)-2
=
The domain then is the set of Real Numbers  .
Using inequality to express this domain,
 and 
(Used "and" because domain is a set and we want to include all members of the set).
Question 757294: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: 9, -i, -8+i
Found 2 solutions by tommyt3rd, stanbon: Answer by tommyt3rd(1112) (Show Source): Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: 9, -i, -8+i
-----
f(x) = (x-9)(x+i)(x-i)(x+8 - i)(x+8 +i)
----
= (x-9)(x^2+1)((x+8)^2+1)
----
= (x-9)(x^2+1)(x^2 + 16x + 65)
------------
etc.
Cheers,
Stan h.
================
Question 756884: Solve the equation in the real number system.
X^4-3x^3+12x^2-48x-64=0
Answer by lwsshak3(6761) (Show Source):
You can put this solution on YOUR website!Solve the equation in the real number system.
X^4-3x^3+12x^2-48x-64=0
***
use rational roots theorem:
...0..|....1.....-3......12....-48.....-64
...1..|....1.....-2......10....-38....-102
...2..|....1.... -1......10....-38....-140
...3..|....1.......0......12....-12...-100
...4..|....1......1.......16.....16.......0 (4 is a root)
====================
...0...|....1......1.......16.....16
..-1..|....1.....0........16......0 (-1 is a root)
f(x)=(x-4)(x+1)(x^2+16x)
roots are:-1, 4,and 2 non-real roots
Question 756946: Find functions f and g such that the given function h can be expressed in the form h=fog
h=(x-3)^2 +x-3 Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!Find functions f and g such that the given function h can be expressed in the form h=fog
h=(x-3)^2 +x-3
----
g(x) = (x-3)^2+x
f(x) = x-3
========
Then h(x) = f[g(x)] = f[(x-3)^2+x] = (x-3)^2+x-3
==============
Cheers,
Stan H.
==============
Question 756881: Use the remainder theorem to find the remainder when f(x) is divided by x+3. Then use the factor theorem to determine whether x+3 is a factor of f(x).
F(x)=3x^6-27x^4+x^2-7
Remainder is______
Answer by sachi(463) (Show Source):
You can put this solution on YOUR website!F(x)=3x^6-27x^4+x^2-7
the divisor is x+3 so the zero of the divisor=-3
now F(-3)=3(-3)^6-27(-3)^4+(-3)^2-7=3*729-27*81+9-7=2
so the Remainder is 2
Question 756890: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: 9, -i, -8+i
F(x)=a_______
Answer by josgarithmetic(1774) (Show Source):
You can put this solution on YOUR website!Just some help but no further:
The needed set of zeros is
{ 9, -i, +i, -8+i, -8-i }
The factored form is 
You have some multiplications and simplifications to do. Avoid extra difficulties through careful pre-simplification and associating:

Continue the multiplications and simplifications.
Question 756872: form a polynomial with real coefficients of degree 2 so that 2+2i is zero Answer by josgarithmetic(1774) (Show Source):
You can put this solution on YOUR website!Degree of 2, possible two zeros, and you must expect the conjugate of your given zero is also a zero. Your TWO zeros are 2+2i AND 2-2i.
Equation is

THE MULTIPLICATION GIVES DIFFERENCE OF TWO SQUARES
EDITED: Corrected mistake.
Question 756643: 3. Find the complex zeros of the polynomial function. Write f in factored form.
F(x)=x^3-8x^2+29x-52
Use the complex zeros to write f in factored form
F(x)=____(reduce fractions and simplify roots)
Answer by Edwin McCravy(8999) (Show Source):
Question 756617: rewrite 6x+24 factored so that the coefficient of x is +1
Please respond as soon as possible, I have a Algebra final exam this Tuesday, but am confuzzled on how to do a problem like this one. Thank you for your time. Answer by josgarithmetic(1774) (Show Source):
Question 756601: Use the rational zero theorem to list all possible rational zeros for the given function
f(x)=x^3-4x^2-19x-14 Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!Use the rational zero theorem to list all possible rational zeros for the given function
f(x)=x^3-4x^2-19x-14
-----
I graphed it and found a zero at x = -1.
Use synthetic division to find the others.
------
-1)....1....-4....-19....-14
.......1....-5....14....|..0
----
Factor the Quotient which is x^2-5x+14
----
= (x-7)(x+2)
------
Zeros are x = -1, -2, 7
==========================
Cheers,
Stan H.
===================
Question 756392: Please help me answer this problem.
For exercise 123 Find f(x+h)-f(x)
Problem 123 is: f(x) = 2x^2 + 3x -4 Found 2 solutions by rothauserc, stanbon: Answer by rothauserc(259) (Show Source):
You can put this solution on YOUR website!we are given:
f(x) = 2x^2 + 3x -4
and we need to find f(x+h) - f(x)
we know f(x) = 2x^2 +3x -4
we need to calculate f(x+h) = 2*(x+h)^2 +3*(x+h) -4
= 2*(x^2+2xh+h^2)+3x+3h-4
= 2x^2+4xh+2h^2+3x+3h-4
now f(x+h) -f(x) =
2x^2+4xh+2h^2+3x+3h-4-2x^2-3x+4
4xh+2h^2+3h
2h^2+4xh+3h
h*(2h+4x+3)
Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website! Find f(x+h)-f(x)
Problem 123 is:
f(x+h) = 2(x+h)^2 + 3(x+h) -4
---
2[x^2+2hx+h^2] + 3x + 3h - 4
----
2x^2 + 4hx + 3x + 2h^2 + 3h - 4
----
f(x+h) = 2x^2 3x + 4hx + 2h^2 + 3h -4
---------
f(x) = 2x^2 + 3x -4
----
Subtract f(x) from f(x+h) to get:
= 4hx + 2h^2 + 3h
==========================
Cheers,
Stan H.
Question 756195: Find the maximum or minimum value of the function. State whether this value is a maximum or minimum.
f(x)= 5x squared - 11
Answer by Theo(3504) (Show Source):
You can put this solution on YOUR website!y = 5x^2 - 11
put in standard form of a quadratic equation to get:
5x^2 - 11 = 0
a = 5
b = 0
c = -11
axis of symmetry is given by the equation:
x = -b/2a
with the given values of b and a, this becomes:
x = 0
the equation is maximum or minimum at x = 0
when x = 0, the value of y is equal to -11
the max/min point is (0,-11)
this point is a minimum because the coefficient of the x^2 term is positive.
the graph is shown below:
Question 755987: y = square root of 16 minus x squared Answer by pragya.ban@gmail.com(30) (Show Source):
You can put this solution on YOUR website!y = square root of 16 minus x squared
I am asuming that it is square root of (16-x^2). As in all under the square root sign. With that being said, let's split it up first to this:
y= square root of 16 + square root of -x^2
y= 4 + -x
y= 4-x
Hope this helps! If not feel free to ask again.
Question 755829: A pond has 2000 fish in it due to a harmful bacteria the fish are dying at a rate of 15% per day write an equation in the form y=a(b)^t .how many fish will there be in the pond in 10 days? How long will it take for half of the fish to die? Answer by reviewermath(604) (Show Source):
You can put this solution on YOUR website!Q:
A pond has 2000 fish in it due to a harmful bacteria the fish are dying at a rate of 15% per day write an equation in the form y=a(b)^t .how many fish will there be in the pond in 10 days? How long will it take for half of the fish to die?
--------------------------------------------------------------------------
A:
Equation: 
In 10 days, there will be  ≈  number of fish.
 = 
t =  =  days
It will take  days for half of the fish to die.
Question 755831: Please I need your help!! Can you find the inverse of the following funtion? Log4 64=x Answer by josmiceli(9817) (Show Source):
You can put this solution on YOUR website!
Do you have trouble reading this?
First of all, repeat over and over:
Logs are exponents
Logs are exponents
Logs are exponents . . .
--------------------
Now you can say in words:
exponent ( some base, the result ) = 
This is telling you that  is an exponent
( some base, . . . ) tells you the base, so
looking at your problem,

You can say:
 = the result
and, the result is  , so

-------------
That's the inverse. If you practice reading these
log equations, I guarantee you'll get better at it.
Question 755842: for the given functions f and g find the specified value of the following functions and state domain of each f(x)=12+9/x ; g(x)=9/x Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!for the given functions f and g find the specified value of the following functions and state domain of each
f(x)=12+(9/x)
x cannot be 0.
Domain: All Real Numbers except x = 0
===========================================
g(x)=9/x
x cannot be 0.
Domain: All Real Numbers except x = 0
=========================================
Cheers,
Stan H.
=====================
Question 755835: Can you please write the recursive rule that describes the following pattern 2,5,8,11..... UU1= Un= and what would be the explicit rule for the pattern you found Answer by stanbon(57967) (Show Source):
You can put this solution on YOUR website!Can you please write the recursive rule that describes the following pattern 2,5,8,11..... UU1= Un= and what would be the explicit rule for the pattern you found
----
1st::: 2
2nd::: 5 = 2+3
3rd::: 8 = 2+2*3
4th::: 11 = 2+3*3
----
a(n) = 2+(n-1)3
=======================
Cheers,
Stan H.
Question 755821: Suppose f(x)=2x-8 and g(x)=1x+11 find (f(-2) and g(f(-2)) Answer by tommyt3rd(1112) (Show Source):
Question 755537: Decide whether or not the equation defines y as a function of x.
What I got:


Is it a function? Answer by josgarithmetic(1774) (Show Source):
You can put this solution on YOUR website!No it does not express y as a function of x. You did actually find part of the equation in the form of y as a function of x. The original equation ALSO has a lower branch which is also a function of x.
Taking square root of  , you have BOTH of these:
 AND
Consistant with that,  IS NOT A FUNCTION.
A reason it is not a function is because for all but one value of x, each value of x gives more than one value of y.
Question 755382: Find the domain of y= square root of x+6. Answer by lwsshak3(6761) (Show Source):
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640
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