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Algebra II : Function Notation

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Example Question #31 : Function Notation

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

Possible Answers:

4x^6

4x^9

$8192x^{27}$

2x^3

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

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 #32 : Function Notation

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 #33 : Function Notation

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

5x+9

6x+9

6x^2+18x

6x+18

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 #31 : 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:

9025

$\frac{1}{9025}$

$\frac{1}{95}$

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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Example Question #38 : Function Notation

Determine $f(\frac{1}{3})$ if $f(x)= \frac{1}{2x}$ .

Possible Answers:

$\frac{1}{6}$

$\frac{3}{2}$

$\frac{3}{7}$

$\frac{7}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

To determine the output of f(x) , substitute the value of $\frac{1}{3}$ as a replacement of .

$f(\frac{1}{3})= \frac{1}{2(\frac{1}{3})} = \frac{1}{\frac{2}{3}}$

Rewrite the complex fraction using a division sign.

$1\div \frac{2}{3}$

Take the reciprocal of the second term and change the division sign to a multiplication sign.

$1\div \frac{2}{3} = 1\times \frac{3}{2}$

The answer is: $\frac{3}{2}$

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Example Question #39 : Function Notation

Determine f(g(3)) if f(x) = 3 and g(x)=3x .

Possible Answers:

Correct answer:

Explanation:

Substitute three into the function of g(x)=3x to solve for g(3) .

g(3)=3(3)=9

Substitute this value into the function f(x) = 3 .

f(9)=3

There is no x-variable to substitute nine, which means the function is equal to three.

The answer is:

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Example Question #40 : Function Notation

If x=4 and y=6 , determine: 2(x+2y)

Possible Answers:

Correct answer:

Explanation:

Substitute the assigned values into the expression.

2(x+2y)=2(4+2(6))

Simplify the inside parentheses.

= 2(4+12) = 2(16) = 32

The answer is:

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Algebra II : Function Notation

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #31 : Function Notation

Example Question #32 : Function Notation

Example Question #33 : Function Notation

Example Question #34 : Function Notation

Example Question #35 : Function Notation

Example Question #31 : Function Notation

Example Question #37 : Function Notation

Example Question #38 : Function Notation

Example Question #39 : Function Notation

Example Question #40 : Function Notation

All Algebra II Resources

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