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Precalculus : Algebra of Functions

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Example Questions

Example Question #21 : Algebra Of Functions

Add the following functions:

(x^2-3x-1)+(4x^2+5x+2)

Possible Answers:

5x^2+2x+1

-3x^2-8x-3

Correct answer:

5x^2+2x+1

Explanation:

To add, simply combine like terms. Thus, the answer is:

5x^2+2x+1

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Example Question #1107 : Pre Calculus

Given the functions: f(x) = 3 and g(x) = 6 , what is f(3)-g(5) ?

Possible Answers:

Correct answer:

Explanation:

For f(3) , substitute the value of inside the function for f(x) and evaluate.

f(3) = 3

For g(5) , substitute the value of inside the function for g(x) and evaluate.

f(5)= 6

Subtract f(3)-g(5) .

f(3)-g(5) = 3-6 = -3

The answer is:

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Example Question #22 : Algebra Of Functions

Simplify $f(x)\cdot g(x)$ given,

f(x)=x^2+2

g(x)=x+6

Possible Answers:

6x^2+12x

x^2+x+8

x^3+6x^2+2x+12

x^3+12

Correct answer:

x^3+6x^2+2x+12

Explanation:

To solve $f(x)\cdot g(x)$ , simply multiply your two functions. Thus,

$\\ f(x)\cdot g(x)=(x^2+2)(x+6)=(x^2)(x)+(6)(x^2)+(2)(x)+(2)(6) \\ \\ =x^3+6x^2+2x+12$

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Example Question #23 : Algebra Of Functions

If $f(x)=\frac{4x-1}{x^2}$ and g(x)=x+1 , find $f\cdot g(x)$ .

Possible Answers:

$\frac{4x+3}{x^2-2x+1}$

$\frac{x+3}{x^2+2x+1}$

$\frac{4x+3}{2x+1}$

$\frac{4x+3}{x^2+2x+1}$

$\frac{4x+3}{x^2+2x-1}$

Correct answer:

$\frac{4x+3}{x^2+2x+1}$

Explanation:

To solve this problem, you must plug in the g function to wherever you see x in the f function. When you plug that in, it looks like this: $\frac{4(x+1)-1}{(x+1)^2}$ . Then simplify so that your answer is: $\frac{4x+3}{x^2+2x+1}$ .

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Example Question #24 : Algebra Of Functions

Find $\left(\frac{f}{g}\right)(x)$ given $f(x)=\frac{1}{x^3}$ and $g(x)=\frac{1}{x^2}$ .

Possible Answers:

$(\frac{f}{g})(x)=\frac{1}{x^2}$

$(\frac{f}{g})(x)=\frac{1}{x^5}$

$(\frac{f}{g})(x)=\frac{1}{x}$

The answer is not present.

$(\frac{f}{g})(x)=\frac{1}{x^6}$

Correct answer:

$(\frac{f}{g})(x)=\frac{1}{x}$

Explanation:

The problem is asking to find the composite function that results when f(x) is divided by g(x).

When dividing fractions, it is important to remember to multiply by the inverse.

$\left(\frac{f}{g}\right)(x)=\frac{\frac{1}{x^3}}{\frac{1}{x^2}}=\frac{1}{x^3}*\frac{x^2}{1}=\frac{1}{x}$

Cross cancel the exponents leaving only one "x" in the bottom.

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Example Question #1 : Composition Of Functions

Suppose f(x) = 9 - x^3 and g(x) = ln (x+1)

What would g(f(x)) be?

Possible Answers:

9 - ln^2(x+1)

ln (9-x^3)

ln (10 - x^3)

10 - ln^3(x + 1)

ln(10 + x - x^3)

Correct answer:

ln (10 - x^3)

Explanation:

Substitute f(x) = 9 -x^3 into the function g(x) = ln (x+1) for .

Then it will become:

g(9 - x^3) = ln ((9-x^3) + 1) = ln (10 - x^3)

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Example Question #2 : Composition Of Functions

$f(x)=3-2x^2+\ln(x)$

g(x)=e^x

What is f(g(x)) ?

Possible Answers:

$3-2e^{2x} +x$

2x^2 +x

3-2e^x +x

3-2x^2+e^x

$3-2e^{2x} +\ln(2e^x)$

Correct answer:

$3-2e^{2x} +x$

Explanation:

f(g(x)) simply means: where ever you see an x in the equation f(x), replace it with g(x).

So, doing just that, we get

$3-2(e^x)^2+\ln(e^x)$ ,

which simplifies to

$3-2e^{2x}+x\ln(e)$ .

Since

$\ln(e)=1$ our simplified expression becomes,

$3-2e^{2x} +x$ .

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Example Question #2 : Composition Of Functions

f(x)=2-5x

$g(x)=\frac{3x^2}{x}-6$

What is g(f(x)) ?

Possible Answers:

-15x

225x^2 +6

12-15x

$\frac{75x}{4}$

-15x+32

Correct answer:

-15x

Explanation:

g(f(x)) simply means replacing every x in g(x) with f(x).

$\frac{3(2-5x)^2}{(2-5x)}-6$

After simplifying, it becomes

$\frac{3(2-5x)(2-5x)}{(2-5x)}-6$

=3(2-5x)-6

=6-15x-6=-15x

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Example Question #3 : Composition Of Functions

For the functions

f(x)=4x

and

g(x)=x^2 .

Evaluate the composite function

$f\circ g$ .

Possible Answers:

DNE

4x^2

8x^3

16x^2

Correct answer:

4x^2

Explanation:

The composite function means to plug in the function of g(x) into the function f(x) for every x value in the function.

Therefore the composition function becomes:

$f\circ g = f[g(x)] = 4(x^2) = 4x^2$ .

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Example Question #4 : Composition Of Functions

For the functions

f(x)=x+4

and

g(x)=x^2 .

Evaluate the composite function

$f\circ g$ .

Possible Answers:

x^2+4

DNE

x^2+x+4

x^2+8x+16

Correct answer:

x^2+4

Explanation:

The composite function means to plug in the function g(x) into f(x) for every x value.

Therefore the composite function becomes,

$f\circ g = f[g(x)] = (x^2)+4 = x^2+4$

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Precalculus : Algebra of Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #21 : Algebra Of Functions

Example Question #1107 : Pre Calculus

Example Question #22 : Algebra Of Functions

Example Question #23 : Algebra Of Functions

Example Question #24 : Algebra Of Functions

Example Question #1 : Composition Of Functions

Example Question #2 : Composition Of Functions

Example Question #2 : Composition Of Functions

Example Question #3 : Composition Of Functions

Example Question #4 : Composition Of Functions

All Precalculus Resources

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