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Algebra 2: Composition of Functions - Printable Mathematics Worksheets - Wayground

Algebra 2: Composition of Functions

16 questions

10th - 12th Grade

Mathematics

Algebra 2: Composition of Functions is a mathematics worksheet for students in Grades 10–12. It focuses on evaluating function expressions and performing operations with functions, including composition-style problems that require students to substitute one function into another and simplify the result. The worksheet contains 16 questions: 15 multiple-choice items and 1 multiple-select item. Students use function notation to determine values from given expressions, carry out indicated operations, and distinguish between related procedures such as composing functions and finding the difference of two functions. The selected-response format gives students practice identifying the correct simplified expression while exposing errors in substitution, operation order, and sign handling. This free printable worksheet includes a complete answer key, making it useful for Algebra 2 practice, independent work, review, or a targeted check of understanding.

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Worksheets

Algebra 2: Composition of Functions

Total questions: 16

Name
Class
Date
1.

If f(x)=2xf\left(x\right)=2x   and  g(x)=2x2−1g\left(x\right)=2x^2-1   find f(g(3))f\left(g\left(3\right)\right)  

a)

34

b)

71

c)

35

d)

142

2.

If f(x)=2xf\left(x\right)=2x   and  g(x)=2x2−1g\left(x\right)=2x^2-1   find g(f(−1))g\left(f\left(-1\right)\right)  

a)

2

b)

15

c)

7

d)

-9

3.

If f(x)=2xf\left(x\right)=2x   and  g(x)=2x2−1g\left(x\right)=2x^2-1   find f(g(x))f\left(g\left(x\right)\right)  

a)

4x2−14x^2-1  

b)

4x2−24x^2-2  

c)

8x2−18x^2-1  

d)

16x2−116x^2-1  

4.

If f(x)=2xf\left(x\right)=2x   and  g(x)=2x2−1g\left(x\right)=2x^2-1   find g(f(x))g\left(f\left(x\right)\right)  

a)

4x2−14x^2-1  

b)

4x2−24x^2-2  

c)

8x2−18x^2-1  

d)

16x2−116x^2-1  

5.

If f(x)=1xf\left(x\right)=\frac{1}{x}   and  g(x)=3x+2g\left(x\right)=3x+2   find (f∘g)(2)\left(f\circ g\right)\left(2\right)  

a)

14\frac{1}{4}  

b)

18\frac{1}{8}  

c)

72\frac{7}{2}  

d)

8

6.

If f(x)=1xf\left(x\right)=\frac{1}{x}   and  g(x)=3x+2g\left(x\right)=3x+2   find (g∘g)(−4)\left(g\circ g\right)\left(-4\right)  

a)

44

b)

-40

c)

-30

d)

-28

7.

If f(x)=1xf\left(x\right)=\frac{1}{x}   and  g(x)=3x+2g\left(x\right)=3x+2   find (g∘f)(x)\left(g\circ f\right)\left(x\right)  

a)

13x+2\frac{1}{3x}+2

b)

3x+23x+2  

c)

3x+2\frac{3}{x}+2  

d)

13x+2\frac{1}{3x+2}  

8.

If f(x)=1xf\left(x\right)=\frac{1}{x}   and  g(x)=3x+2g\left(x\right)=3x+2   find f(g(x))f\left(g\left(x\right)\right)  

a)

13x+2\frac{1}{3x}+2

b)

3x+23x+2  

c)

3x+2\frac{3}{x}+2  

d)

13x+2\frac{1}{3x+2}  

9.

If f(x)=x2f\left(x\right)=x^2   and  g(x)=xg\left(x\right)=\sqrt{x}   find g(f(x))g\left(f\left(x\right)\right)  

a)

x4x^4  

b)

xx  

c)

x\sqrt[]{x}  

d)

x2x^2  

10.

If f(x)=x2f\left(x\right)=x^2   and  g(x)=1x2g\left(x\right)=\frac{1}{x^2}   find (f∘g)(−1)\left(f\circ g\right)\left(-1\right)  

a)

14\frac{1}{4}  

b)

11

c)

−1-1  

d)

−14-\frac{1}{4}  

11.

When f(x)=x2+9f(x)=x^2+9   and g(x)=x−9g(x)=x-9  , find f(x)−g(x)f(x)-g(x)  

a)

x2+x+9x^2+x+9  

b)

x2−x+9x^2-x+9  

c)

x2−xx^2-x  

d)

x2−x+18x^2-x+18  

12.

When f(x)=9−3xf(x)=9-3x   and g(x)=5x−7g(x)=5x-7   , find f(x)+g(x)f(x)+g(x)  

a)

14x−1014x-10  

b)

−8x+2-8x+2  

c)

2x+22x+2  

d)

2x−22x-2  

13.

If g(x)=x2+6g\left(x\right)=x^2+6   and f(x)=2x−4f\left(x\right)=2x-4  , find g(f(x))g\left(f\left(x\right)\right)  

a)

2x2−12x−42x^2-12x-4  

b)

2x2+12x−42x^2+12x-4  

c)

4x2−16x+224x^2-16x+22  

d)

x3−2x2+1x^3-2x^2+1  

14.

Perform the indicated operation.

a)

A

b)

B

c)

C

d)

D

15.
f(n)=x2+1
g(n)=2x-5
Find f(n)-g(n)
a)
x2-2x+6
b)
-x2+2x+4
c)
-x2-2x-6
d)
x2-2x-4
16.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

Answer Key

Algebra 2: Composition of Functions

Total questions: 16

1.
a)

34

2.
c)

7

3.
b)

4x2−24x^2-2  

4.
c)

8x2−18x^2-1  

5.
b)

18\frac{1}{8}  

6.
d)

-28

7.
c)

3x+2\frac{3}{x}+2  

8.
d)

13x+2\frac{1}{3x+2}  

9.
b)

xx  

10.
b)

11

11.
d)

x2−x+18x^2-x+18  

12.
c)

2x+22x+2  

13.
c)

4x2−16x+224x^2-16x+22  

14.
a)

A

15.
a) x2-2x+6
16.
c)

92

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FAQs

What does this Algebra 2 composition of functions worksheet cover?

This worksheet practices evaluating function expressions, composing functions through substitution, and performing indicated operations with functions. Its 15 multiple-choice questions and 1 multiple-select question require students to select or identify the resulting value or simplified expression, including a function-difference problem.

How can I use this worksheet to teach composition of functions?

First model how to read the function notation and substitute one function into another, keeping parentheses around the entire inner expression. Then have students complete the composition and function-operation questions, asking them to explain which expression they substituted and how they simplified it. Use the multiple-select item as a discussion prompt about why more than one response may or may not satisfy the indicated operation.

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

Watch for students reversing the order of the functions in a composition or substituting only part of the inner expression. Other common errors include dropping parentheses, mishandling negative signs while simplifying, and confusing a function difference such as f(n) − g(n) with composition. The multiple-choice options can help you identify which step produced the error.

How do I assign and grade this composition of functions worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key. For printable submissions, you can scan student work with the Wayground for Teachers app to help grade responses. The PDF option can also support schools that want to reduce screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the function notation, parentheses, and answer choices are easier to follow. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the composition and function-operation questions.

Where can I find more free worksheets like this on Wayground?

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

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