Worksheets · Algebra 2

Composition of functions worksheet

A composition feeds the output of one function into the other. For f(g(x)) you work the inside one first, then put the whole result wherever x appears in f. The order matters: f(g(x)) and g(f(x)) are usually different functions.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets

Name

Composition of Functions

Date Period

Find each composition.

  1. Given f(x)=6x+1 and g(x)=6x+3, find f(g(x))
  2. Given f(x)=−5x−9 and g(x)=−4x−4, find f(g(x))
  3. Given f(x)=−6x−1 and g(x)=−5x−2, find f(g(x))
  4. Given f(x)=−4x+8 and g(x)=4x+5, find f(g(x))
  5. Given f(x)=6x+5 and g(x)=−4x−7, find f(g(x))
  6. Given f(x)=−6x−3 and g(x)=−4x+2, find f(g(x))
  7. Given f(x)=−6x+8 and g(x)=−6x+4, find f(g(x))
  8. Given f(x)=6x+9 and g(x)=−4x+9, find f(g(x))
  9. Given f(x)=5x+3 and g(x)=−6x+7, find f(g(x))
  10. Given f(x)=4x+2 and g(x)=−4x−2, find f(g(x))
  11. Given f(x)=4x+5 and g(x)=−4x+8, find f(g(x))
  12. Given f(x)=−4x−9 and g(x)=−4x+5, find f(g(x))
  13. Given f(x)=−6x−1 and g(x)=5x+2, find f(g(x))
  14. Given f(x)=−6x−8 and g(x)=−4x+8, find f(g(x))
  15. Given f(x)=−6x−9 and g(x)=−6x+1, find f(g(x))
  16. Given f(x)=−4x+8 and g(x)=4x−4, find f(g(x))
  17. Given f(x)=6x+3 and g(x)=−5x+7, find f(g(x))
  18. Given f(x)=−6x−2 and g(x)=−4x+2, find f(g(x))
  19. Given f(x)=−4x−8 and g(x)=−6x−8, find f(g(x))
  20. Given f(x)=5x+4 and g(x)=6x−5, find f(g(x))

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Composition of FunctionsAnswer keyVersion 1

Date Period

Find each composition.

  1. Given f(x)=6x+1 and g(x)=6x+3, find f(g(x))36x+19
  2. Given f(x)=−5x−9 and g(x)=−4x−4, find f(g(x))20x+11
  3. Given f(x)=−6x−1 and g(x)=−5x−2, find f(g(x))30x+11
  4. Given f(x)=−4x+8 and g(x)=4x+5, find f(g(x))−16x−12
  5. Given f(x)=6x+5 and g(x)=−4x−7, find f(g(x))−24x−37
  6. Given f(x)=−6x−3 and g(x)=−4x+2, find f(g(x))24x−15
  7. Given f(x)=−6x+8 and g(x)=−6x+4, find f(g(x))36x−16
  8. Given f(x)=6x+9 and g(x)=−4x+9, find f(g(x))−24x+63
  9. Given f(x)=5x+3 and g(x)=−6x+7, find f(g(x))−30x+38
  10. Given f(x)=4x+2 and g(x)=−4x−2, find f(g(x))−16x−6
  11. Given f(x)=4x+5 and g(x)=−4x+8, find f(g(x))−16x+37
  12. Given f(x)=−4x−9 and g(x)=−4x+5, find f(g(x))16x−29
  13. Given f(x)=−6x−1 and g(x)=5x+2, find f(g(x))−30x−13
  14. Given f(x)=−6x−8 and g(x)=−4x+8, find f(g(x))24x−56
  15. Given f(x)=−6x−9 and g(x)=−6x+1, find f(g(x))36x−15
  16. Given f(x)=−4x+8 and g(x)=4x−4, find f(g(x))−16x+24
  17. Given f(x)=6x+3 and g(x)=−5x+7, find f(g(x))−30x+45
  18. Given f(x)=−6x−2 and g(x)=−4x+2, find f(g(x))24x−14
  19. Given f(x)=−4x−8 and g(x)=−6x−8, find f(g(x))24x+24
  20. Given f(x)=5x+4 and g(x)=6x−5, find f(g(x))30x−21

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Given f(x)=2x+1 and g(x)=x−3, find f(g(x))

  1. g(x) is x minus 3.
  2. Put that in place of x in f: 2(x - 3) + 1.
  3. Expand: 2x - 6 + 1.

The answer is 2x−5.

Where students go wrong

Multiplying the two functions instead of nesting them. f(g(x)) is not f(x) times g(x). And swapping the order changes the answer, so read which one is inside.

Also called composite functions, f of g of x or composing functions.

What you can put on this worksheet

Compose two functions
Given f(x)=x+3 and g(x)=−3x−3, find f(g(x)) → −3x
Write h as f(g(x))
If h(x)=f(g(x)) and h(x)=x+6, find f(x) and g(x), neither equal to x → f(x)=x, g(x)=x+6

Questions about these worksheets

Yes. Every composition of functions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the composition of functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: compose two functions and write h as f(g(x)). Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying the two functions instead of nesting them. f(g(x)) is not f(x) times g(x). And swapping the order changes the answer, so read which one is inside.