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finding inverse of a function 2 - Printable Math Worksheets 10th - 12th Grade - Wayground

finding inverse of a function 2

Ayman Aziz

Created by Ayman Aziz

12 questions

10th - 12th Grade

Math

Updated Sep 2026

This Grade 10–12 mathematics worksheet helps students understand and find the inverse of a function. It begins with a multiple-choice question about the defining idea of an inverse—switching the x- and y-values—then provides 11 additional multiple-choice items in which students identify inverse functions from given choices. The repeated format gives students focused practice recognizing the correct algebraic relationship between a function and its inverse. Use this resource for independent practice, a guided review, homework, or a quick formative assessment after introducing inverse functions. Reviewing the answer choices with students can reveal whether they understand the meaning of an inverse or are confusing it with operations such as making values negative or dividing by a number. This free printable worksheet includes a complete answer key for efficient checking and feedback.

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finding inverse of a function 2

Total questions: 12

Name
Class
Date
1.
What does it mean to find the inverse of a function?
a)
the x's and y's are switched
b)
the x's and y's are divided by 2
c)
the x's and y's are made negative
d)
the x's and y's are the same
2.

Find the inverse of f(x)=3x+2f\left(x\right)=3x+2  

a)

f−1(x)=x−23f^{-1}\left(x\right)=\frac{x-2}{3}  

b)

f−1(x)=x−32f^{-1}\left(x\right)=\frac{x-3}{2}  

c)

f−1(x)=3x2f^{-1}\left(x\right)=\frac{3x}{2}  

d)

f−1(x)=2+x3f^{-1}\left(x\right)=\frac{2+x}{3}  

3.

Find the inverse of f(x)=−5x−7f\left(x\right)=-5x-7  

a)

f−1(x)=5x+7−7f^{-1}\left(x\right)=\frac{5x+7}{-7}  

b)

f−1(x)=x+57f^{-1}\left(x\right)=\frac{x+5}{7}  

c)

f−1(x)=x+7−5f^{-1}\left(x\right)=\frac{x+7}{-5}  

d)

f−1(x)=7−5+xf^{-1}\left(x\right)=\frac{7}{-5+x}  

4.

Find the inverse of f(x)=12x−3f\left(x\right)=12x-3  

a)

f−1(x)=x+312f^{-1}\left(x\right)=\frac{x+3}{12}  

b)

f−1(x)=x−312f^{-1}\left(x\right)=\frac{x-3}{12}  

c)

f−1(x)=x+123f^{-1}\left(x\right)=\frac{x+12}{3}  

d)

f−1(x)=x−123f^{-1}\left(x\right)=\frac{x-12}{3}  

5.

Find the inverse of f(x)=−34x+5f\left(x\right)=-\frac{3}{4}x+5  

a)

f−1(x)=5(x−43)f^{-1}\left(x\right)=5\left(x-\frac{4}{3}\right)  

b)

f−1(x)=−34(x−5)f^{-1}\left(x\right)=-\frac{3}{4}\left(x-5\right)  

c)

f−1(x)=−43(x−5)f^{-1}\left(x\right)=-\frac{4}{3}\left(x-5\right)  

d)

f−1(x)=−5(x−34)f^{-1}\left(x\right)=-5\left(x-\frac{3}{4}\right)  

6.

Find the inverse of f(x)=12x+8f\left(x\right)=\frac{1}{2}x+8  

a)

f−1(x)=2x+8f^{-1}\left(x\right)=2x+8  

b)

f−1(x)=2x−16f^{-1}\left(x\right)=2x-16  

c)

f−1(x)=2(x+8)f^{-1}\left(x\right)=2\left(x+8\right)  

d)

f−1(x)=12x−16f^{-1}\left(x\right)=\frac{1}{2}x-16  

7.

Find the inverse of f(x)=x2+5f\left(x\right)=x^2+5  

a)

f−1(x)=x−25f^{-1}\left(x\right)=x-25  

b)

f−1(x)=5+xf^{-1}\left(x\right)=\sqrt{5+x}  

c)

f−1(x)=x−5f^{-1}\left(x\right)=\sqrt{x-5}  

d)

f−1(x)=x−5f^{-1}\left(x\right)=\sqrt{x}-5  

8.

Find the inverse of f(x)=x2−4f\left(x\right)=x^2-4  

a)

f−1(x)=x+16f^{-1}\left(x\right)=\sqrt{x+16}  

b)

f−1(x)=x−4f^{-1}\left(x\right)=\sqrt{x-4}  

c)

f−1(x)=x+4f^{-1}\left(x\right)=\sqrt{x}+4  

d)

f−1(x)=x+4f^{-1}\left(x\right)=\sqrt{x+4}  

9.

Find the inverse of f(x)=(x−6)2f\left(x\right)=\left(x-6\right)^2  

a)

f−1(x)=x+6f^{-1}\left(x\right)=\sqrt{x}+6  

b)

f−1(x)=x+6f^{-1}\left(x\right)=\sqrt{x+6}  

c)

f−1(x)=x−6f^{-1}\left(x\right)=\sqrt{x}-6  

d)

f−1(x)=x−6f^{-1}\left(x\right)=\sqrt{x-6}  

10.

Find the inverse of f(x)=x−2f\left(x\right)=\sqrt{x-2}  

a)

f−1(x)=x2−2f^{-1}\left(x\right)=x^2-2  

b)

f−1(x)=x2+2f^{-1}\left(x\right)=x^2+2  

c)

f−1(x)=(x+2)2f^{-1}\left(x\right)=\left(x+2\right)^2  

d)

f−1(x)=(x−2)2f^{-1}\left(x\right)=\left(x-2\right)^2  

11.

Find the inverse of f(x)=x+8f\left(x\right)=\sqrt{x}+8  

a)

f−1(x)=x2+8f^{-1}\left(x\right)=x^2+8  

b)

f−1(x)=x2−8f^{-1}\left(x\right)=x^2-8  

c)

f−1(x)=(x+8)2f^{-1}\left(x\right)=\left(x+8\right)^2  

d)

f−1(x)=(x−8)2f^{-1}\left(x\right)=\left(x-8\right)^2  

12.

Find the inverse of f(x)=x−3+4f\left(x\right)=\sqrt{x-3}+4  

a)

f−1(x)=x2+4f^{-1}\left(x\right)=x^2+4  

b)

f−1(x)=x2−8f^{-1}\left(x\right)=x^2-8  

c)

f−1(x)=(x−4)2+3f^{-1}\left(x\right)=\left(x-4\right)^2+3  

d)

f−1(x)=(x−4)2−3f^{-1}\left(x\right)=\left(x-4\right)^2-3  

WaygroundAnswer Key

finding inverse of a function 2

Total questions: 12

1.
a) the x's and y's are switched
2.
a)

f−1(x)=x−23f^{-1}\left(x\right)=\frac{x-2}{3}  

3.
c)

f−1(x)=x+7−5f^{-1}\left(x\right)=\frac{x+7}{-5}  

4.
a)

f−1(x)=x+312f^{-1}\left(x\right)=\frac{x+3}{12}  

5.
c)

f−1(x)=−43(x−5)f^{-1}\left(x\right)=-\frac{4}{3}\left(x-5\right)  

6.
b)

f−1(x)=2x−16f^{-1}\left(x\right)=2x-16  

7.
c)

f−1(x)=x−5f^{-1}\left(x\right)=\sqrt{x-5}  

8.
d)

f−1(x)=x+4f^{-1}\left(x\right)=\sqrt{x+4}  

9.
a)

f−1(x)=x+6f^{-1}\left(x\right)=\sqrt{x}+6  

10.
b)

f−1(x)=x2+2f^{-1}\left(x\right)=x^2+2  

11.
d)

f−1(x)=(x−8)2f^{-1}\left(x\right)=\left(x-8\right)^2  

12.
c)

f−1(x)=(x−4)2+3f^{-1}\left(x\right)=\left(x-4\right)^2+3  

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FAQs

What does this worksheet cover, and how does it help students find inverse functions?

This worksheet covers finding the inverse of a function through 12 multiple-choice questions. Students first identify that an inverse switches the x- and y-values, then apply that idea to select inverse functions in 11 additional items, strengthening recognition of the inverse relationship.

How can I use this worksheet to teach students to find an inverse of a function?

Begin by using the first question to discuss what it means to switch the x- and y-values when finding an inverse. Model the process with a function, explain how the switched relationship appears in the answer choices, and then have students complete the remaining multiple-choice items while justifying why their selected function represents the inverse.

What mistakes should I watch for when students complete this inverse-functions worksheet?

Watch for students who confuse an inverse function with making the x- and y-values negative, dividing them by 2, or treating them as equal; these misconceptions appear among the choices in the introductory item. In the remaining inverse-function questions, check whether students are identifying the switched relationship rather than selecting an expression based on a superficial change to the original function.

How do I assign and grade this inverse-functions worksheet?

This 12-question worksheet is available as a printable PDF and as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support classrooms that are reducing screen time.

How can I differentiate this multiple-choice inverse-functions worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the 12 multiple-choice items are easier to read and navigate. You can also apply a dyslexia-friendly font or translate the inverse-functions worksheet into another language when those options support your learners.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, including downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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