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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #27 : Function Notation

Given f(x) = 3x+3 and g(x)=-3 , what is g(f(x))+2g(x) ?

Possible Answers:

$\textup{The answer cannot be determined.}$

Correct answer:

Explanation:

Evaluate g(f(x)) first. If we plugged in the function f(x) = 3x+3 into the function g(x)=-3 , no matter what is replaced with, the final output will always be negative three.

g(3x+3)= -3

Evaluate 2g(x) . Multiply the function g(x)=-3 by two.

2g(x) = -6

Sum both numbers.

-3+(-6) = -3-6=-9

The answer is:

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Example Question #28 : Function Notation

If g(x)=1 , f(x)=2 , and $h(x)= \pi$ , what is 2f(g(x))+h(g(x)) ?

Possible Answers:

$\pi+1$

$\pi+2$

$2\pi+4$

$\pi +4$

$2\pi+2$

Correct answer:

$\pi +4$

Explanation:

Evaluate each term separately.

The term f(g(x)) means to input the function g(x)=1 into the function f(x) .

$2f(g(x)) = 2\cdot f(1) = 2\cdot 2 = 4$

Follow suit for h(g(x)) . Substitute g(x)=1 into the function h(x) .

$h(g(x)) =h(1)=\pi$

Add the two known terms.

$2f(g(x))+h(g(x)) = 4+\pi$

The answer is: $\pi +4$

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Example Question #29 : Function Notation

If g(x)=3x+5 , what is g(x+3) ?

Possible Answers:

3x+8

3x+11

3x+14

3x+55

3x+5

Correct answer:

3x+14

Explanation:

In order to solve g(x+3) , replace the entire quantity of (x+3) as a replacement of .

Replace the term.

g(x+3)=3(x+3)+5

Distribute the binomial.

3x+9+5 = 3x+14

The answer is: 3x+14

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Example Question #151 : Functions And Graphs

If h(x) = 2x^3 , what is h(h(2x^3)) ?

Possible Answers:

$\textup{The answer is not given.}$

$8192x^{27}$

2x^3

4x^9

4x^6

Correct answer:

$8192x^{27}$

Explanation:

Evaluate h(2x^3) first. Substitute 2x^3 into the function as a replacement of the x-variable.

h(2x^3) = 2(2x^3)^3 = 2(8x^9) = 16x^9

Substitute this value to determine h(h(2x^3)) .

h(h(2x^3)) = h(16x^9) = 2(16x^9)^3=2(16x^9)(16x^9)(16x^9)

The answer is: $8192x^{27}$

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Example Question #681 : Algebra Ii

Given the function g(x)= 2x^3-6x , what is the value of g(-3) ?

Possible Answers:

Correct answer:

Explanation:

Substitute negative three into the function.

g(-3)= 2(-3)^3-6(-3)

Simplify this equation by order of operations.

2(-3)^3-6(-3) = 2(-27)+18 = -54+18

The answer is:

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Example Question #161 : Introduction To Functions

If f(x) = 6x+6 , find $f^{-1}(6)$ .

Possible Answers:

$\frac{1}{6}$

$-\frac{1}{6}$

Correct answer:

Explanation:

To solve this question, first convert the given function to its inverse.

Rewrite f(x) = 6x+6 by replacing f(x) with .

y= 6x+6

Interchange the x and y variables.

x=6y+6

Solve for y. Subtract 6 from both sides.

x-6=6y+6-6

Simplify, and divide by 6 on both sides.

$\frac{x-6}{6}=\frac{6y}{6}$

Simplify both sides.

The inverse function is: $y= f^{-1}(x)= \frac{1}{6}x-1$

Solve for $f^{-1}(6)$ by plugging 6 into the inverse function.

$\frac{1}{6}(6)-1 = 1-1=0$

The answer is:

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Example Question #34 : Function Notation

Given the following function, determine f(2x) if: f(x) = 3x+9

Possible Answers:

6x^2+9

6x+18

5x+9

6x^2+18x

6x+9

Correct answer:

6x+9

Explanation:

Input (2x) as the replacement of the x-variable for the function f(x) .

The equation becomes:

f(2x) = 3(2x)+9

Simplify by distribution.

The answer is: 6x+9

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Example Question #35 : Function Notation

Determine $f^{-1}(3)$ if f(x) = 3x+3 .

Possible Answers:

$-\frac{2}{3}$

$\frac{2}{3}$

$\frac{1}{3}$

$-\frac{1}{3}$

Correct answer:

Explanation:

Replace the f(x) with .

y= 3x+3

Interchange the x and y variables.

x= 3y+3

Subtract three from both sides.

x-3= 3y+3-3

x-3= 3y

Divide by three on both sides.

$\frac{x-3}{3}=\frac{ 3y}{3}$

The inverse function is: $y=\frac{1}{3}x-1$

Substitute $f^{-1}(3)$ as a replacement of .

$y=\frac{1}{3}(3)-1 = 1-1 = 0$

The answer is:

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Example Question #36 : Function Notation

Given the function f(x)= 5x-5 , what is: $f(-\frac{1}{5})$ ?

Possible Answers:

$-\frac{9}{2}$

$-\frac{11}{2}$

$-\frac{26}{5}$

Correct answer:

Explanation:

Replace x with negative one-fifth.

$f(-\frac{1}{5})= 5(-\frac{1}{5})-5$

Simplify the expression. When a number is subtracted from a

-1-5 = -6

The answer is .

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Example Question #37 : Function Notation

Evaluate $g(f(\frac{1}{95}))$ if: g(x) = 95 and $f(x) = \frac{1}{95}$

Possible Answers:

$\frac{1}{9025}$

9025

$\frac{1}{95}$

Correct answer:

Explanation:

Evaluate $g(f(\frac{1}{95}))$ by solving for $f(\frac{1}{95})$ first.

No matter what value of , $f(x) = \frac{1}{95}$ . This means that:

$f( \frac{1}{95}) = \frac{1}{95}$

Then:

$g(\frac{1}{95})$

For any value of , g(x) = 95 . This means that:

$g(\frac{1}{95}) = 95$

The answer is:

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #27 : Function Notation

Example Question #28 : Function Notation

Example Question #29 : Function Notation

Example Question #151 : Functions And Graphs

Example Question #681 : Algebra Ii

Example Question #161 : Introduction To Functions

Example Question #34 : Function Notation

Example Question #35 : Function Notation

Example Question #36 : Function Notation

Example Question #37 : Function Notation

All Algebra II Resources

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