Algebra 2 Inverse Functions Quiz – Free PDF

Contents

This algebra 2 inverse functions quiz asks 10 multiple-choice questions on function operations, composition and inverses, and each answer comes with a short explanation.

Ten multiple-choice questions on function operations, composition, and inverse functions. Choose the single best answer, and use graphs, composition checks, and domain restrictions to confirm your choice. Each explanation shows the idea and the most common mistake.

Algebra 2Common Core: F-BF.A.1b · F-BF.A.1c · F-BF.B.4a

🎯 Function Operations, Composition and Inverses – Algebra 2 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

Let \(f(x)=x^{2}-4x\) and \(g(x)=3x+2\). What is \((f+g)(x)\)?

A \(x^{2}-7x-2\)

B \(x^{2}-x-2\)

C \(x^{2}-x+2\)

D \(x^{2}+7x+2\)

Question 2

Let \(f(x)=2x+3\) and \(g(x)=x^{2}-1\). What is \(f(g(2))\)?

A \(48\)

B \(10\)

C \(21\)

D \(9\)

Question 3

What is the inverse of \(f(x)=3x-6\)?

A \(f^{-1}(x)=\frac{x+6}{3}\)

B \(f^{-1}(x)=\frac{x}{3}+6\)

C \(f^{-1}(x)=\frac{x-6}{3}\)

D \(f^{-1}(x)=-3x+6\)

Question 4

Which line is the graph of \(f^{-1}\)?

The graph of f (blue) and four candidate lines.

A Line A

B Line B

C Line C

D Line D

Question 5

Let \(f(x)=\sqrt{x}\) and \(g(x)=x+6\). What is the domain of \(f(g(x))\)?

A \(x\ge 6\)

B \(x\ge -6\)

C \(x\ge 0\)

D \(x\le -6\)

Question 6

Which pair of functions are inverses of each other?

A \(f(x)=4x+1\) and \(g(x)=\frac{x+1}{4}\)

B \(f(x)=4x+1\) and \(g(x)=\frac{x-1}{4}\)

C \(f(x)=4x+1\) and \(g(x)=\frac{1}{4x+1}\)

D \(f(x)=4x+1\) and \(g(x)=-4x-1\)

Question 7

The graph shows \(f(x)=(x-1)^{2}-2\). Which domain restriction makes \(f\) one-to-one?

The graph of f(x) = (x − 1)² − 2.

A \(x\ge -2\)

B \(-1\le x\le 3\)

C \(x\ge 1\)

D all real numbers

Question 8

Using the graph of \(f(x)=x^{2}-1\) for \(x\ge 0\), what is \(f^{-1}(3)\)?

The graph of f(x) = x² − 1 for x ≥ 0.

A \(8\)

B \(10\)

C \(\sqrt{2}\)

D \(2\)

Question 9

The radius of a circle is \(r(t)=4t\) and its area is \(A(r)=\pi r^{2}\). What is \(A(r(t))\)?

A \(4\pi t^{2}\)

B \(16\pi t^{2}\)

C \(16\pi^{2}t^{2}\)

D \(8\pi t^{2}\)

Question 10

Let \(f(x)=x+2\) and \(g(x)=x-5\). What is \((fg)(x)\)?

A \(x^{2}+3x-10\)

B \(2x-3\)

C \(x^{2}-10\)

D \(x^{2}-3x-10\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Composition: (f ∘ g)(x) = f(g(x)); the inner function g runs first and order usually matters.
Inverse method: write y = f(x), swap x and y, solve for y, rename it f⁻¹(x).
Two functions are inverses when f(g(x)) = x and g(f(x)) = x for every x in the domains.
The graph of f⁻¹ is the reflection of the graph of f across the line y = x; points (a, b) become (b, a).
Only one-to-one functions have inverses; restrict the domain (such as x ≥ 0 for x²) when needed.