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

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

Question 758959: Find the domain:
f(x)=3x^(2)+1

You can put this solution on YOUR website!
This is a polynomial. All polynomials have the same domain: the set of all real numbers.

x = 1 -y^2

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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)
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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.

-3< 2x-1/5 < 0
This sign -> / means 2x-1 is over 5, as a fraction. < 0 is not a part of the fraction

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-3< (2x-1)/5 < 0
---------
-15 < 2x-1 < 0
---------
-14 < 2x < 1
------
-7 < x < 1/2
==================
Cheers,
Stan H.

Question 758848: Solve -1<2-x<4
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Solve -1<2-x<4
-----
-3 < -x < 2
-----
-2 < x < 3
================
Cheers,
Stan H.
=============

You can put this solution on YOUR website!
solve |3x|+4< 34
------
|3x| < 30
-----
-30 < 3x < 30
----
-10 < x < 10
================
Cheers,
Stan H.
================

Question 758743: What is the domain of this function: g(t)=9/sqrt5t+20 ?
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:
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If f(x)=x^2+1, find f(a+1)
-----
f(a+1) = (a+1)^2 + 1 = a^2 + 2a + 2
==============================
Cheers,
Stan H.
===============

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

Given functions f(x) = 3x and g(x) =x-5, find (f of g)(x)

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(f of g)(x)= f(g(x))=f(x-5)=3(x-5)

:)

If f(x) = x^2 - 2x + 3, find f(x + 2)

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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
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Assuming you mean N to be the natural numbers i.e. {1,2,3,...} then
ranf={1}

Question 758242: The range of the function f: N→N defined by f(x)= (-1)^x-1
Found 2 solutions by tommyt3rd, stanbon:
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Assuming you mean N to be the natural numbers i.e. {1,2,3,...} then
ranf={1}

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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)

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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

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What is the value of f(x)=36^x when x=1/2?
---------------
=
=
= 6

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?

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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.

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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 ____

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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___

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e^x=13.7
-----------
x = ln(13.7)

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:
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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.
:-)

You can put this solution on YOUR website!
5/(3x^2y) - 4/(6xy^3) =(5*2y^2-4*x)/(6x^2y^3) =(10y^2-4x)/6x^2y^3
=(5y^2-2x)/3x^y^3
Thanks

Simplify the expression:
(x^2+3x+2)/(x+2)
Thanks

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(x^2+3x+2)/(x+2)=(x^2+x+2x+2)/(x+2)=[x(x+1)+2(x+1)]/(x+2)=(x+2)(x+1)/(x+2)
=(x+1)

Question 757410: find the domain of (f + g)(x)when f(x) =2x+5and g (x)=4/x-2
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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:
You can put this solution on YOUR website!
The general polynomial with these roots is:

let a=1, then

:)

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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

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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

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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______

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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_______

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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
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):
You can put this solution on YOUR website!
```F(x)=x^3-8x^2+29x-52

The possible rational zeros are ± the factors of 52,
which are ±1,±2,±4,±13,±26, and ±52

You can keep trying those and the only one that gives
a zero remainder and is therefore a rational zero is 4.

4|1 -8  29 -52
|   4 -16  52
1 -4  13   0

So we have factored F(x) this way:

F(x) = (x-4)(x²-4x+13)

To find the other zeros we set the factor
x² - 4x + 13 = 0 and use the quadratic formula:

x =

x =

x =

x =

x =

x =

x =

x = 2 ± 3i

So the other zeros are 2 + 3i and 2 - 3i

So the factored form of F(x) is

F(x) = (x - 4)[x - (2 + 3i)][x - (2 - 3i)]

or

F(x) = (x - 4)(x - 2 - 3i)(x - 2 + 3i)

Edwin```

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.

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Refer to this:

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

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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.
===================

For exercise 123 Find f(x+h)-f(x)
Problem 123 is: f(x) = 2x^2 + 3x -4

Found 2 solutions by rothauserc, stanbon:
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)

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

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
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?
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
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

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
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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
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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))
You can put this solution on YOUR website!
f(-2)=2(-2)-8=4--8=-12

g(f(-2))=g(-12)= 1(-12)+11=-12+11=-1

:)

Question 755537: Decide whether or not the equation defines y as a function of x.

What I got:

Is it a function?

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.