Worksheets · Algebra 2

Function operations and inverses worksheet

Combining two functions, and undoing one. Composition is the one worth drilling: f(g(x)) means g happens first, which is the opposite of how it reads.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Function Operations and Inverses

Date Period

Answer each question.

  1. Given f(x)=6x+1 and g(x)=6x+3, find (f+g)(x)
  2. Given f(x)=−4x+5 and g(x)=−5x−3, find f(g(x))
  3. Find the inverse of f(x)=−14x−10
  4. Given f(x)=6x−4 and g(x)=5x−2, find (fg)(x)
  5. Given f(x)=−6x−7 and g(x)=4x+3, find f(g(x))
  6. Find the inverse of f(x)=−15x−16
  7. Given f(x)=−4x+2 and g(x)=−6x+8, find (fg)(x)
  8. Given f(x)=6x−3 and g(x)=6x+7, find f(g(x))
  9. Find the inverse of f(x)=9x+17
  10. Given f(x)=6x+5 and g(x)=4x−7, find (fg)(x)
  11. Given f(x)=−5x−4 and g(x)=5x−6, find f(g(x))
  12. Find the inverse of f(x)=−21x−10
  13. Given f(x)=−4x−9 and g(x)=−4x+5, find (f+g)(x)
  14. Given f(x)=5x−3 and g(x)=4x−5, find f(g(x))
  15. Find the inverse of f(x)=12x+20
  16. Given f(x)=−6x−2 and g(x)=4x−7, find (f+g)(x)
  17. Given f(x)=4x+8 and g(x)=−5x−2, find f(g(x))
  18. Find the inverse of f(x)=−23x+18
  19. Given f(x)=−5x+7 and g(x)=−6x−2, find (fg)(x)
  20. Given f(x)=−4x−3 and g(x)=−4x+4, find f(g(x))

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

Sigma Prep · sigmaprep.io/worksheets

Name

Function Operations and InversesAnswer keyVersion 1

Date Period

Answer each question.

  1. Given f(x)=6x+1 and g(x)=6x+3, find (f+g)(x)12x+4
  2. Given f(x)=−4x+5 and g(x)=−5x−3, find f(g(x))20x+17
  3. Find the inverse of f(x)=−14x−10f−1(x)=−x−1014
  4. Given f(x)=6x−4 and g(x)=5x−2, find (fg)(x)30x2−32x+8
  5. Given f(x)=−6x−7 and g(x)=4x+3, find f(g(x))−24x−25
  6. Find the inverse of f(x)=−15x−16f−1(x)=−x−1615
  7. Given f(x)=−4x+2 and g(x)=−6x+8, find (fg)(x)24x2−44x+16
  8. Given f(x)=6x−3 and g(x)=6x+7, find f(g(x))36x+39
  9. Find the inverse of f(x)=9x+17f−1(x)=x−179
  10. Given f(x)=6x+5 and g(x)=4x−7, find (fg)(x)24x2−22x−35
  11. Given f(x)=−5x−4 and g(x)=5x−6, find f(g(x))−25x+26
  12. Find the inverse of f(x)=−21x−10f−1(x)=−x−1021
  13. Given f(x)=−4x−9 and g(x)=−4x+5, find (f+g)(x)−8x−4
  14. Given f(x)=5x−3 and g(x)=4x−5, find f(g(x))20x−28
  15. Find the inverse of f(x)=12x+20f−1(x)=x−2012
  16. Given f(x)=−6x−2 and g(x)=4x−7, find (f+g)(x)−2x−9
  17. Given f(x)=4x+8 and g(x)=−5x−2, find f(g(x))−20x
  18. Find the inverse of f(x)=−23x+18f−1(x)=−x+1823
  19. Given f(x)=−5x+7 and g(x)=−6x−2, find (fg)(x)30x2−32x−14
  20. Given f(x)=−4x−3 and g(x)=−4x+4, find f(g(x))16x−19

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

How to do these

Given f(x)=2x+1 and g(x)=x−4, find f(g(x))

  1. g happens first, so start with x - 4.
  2. Put that into f in place of x.
  3. 2(x - 4) + 1.

The answer is 2x−7.

Where students go wrong

Doing the functions in the order they are written. f(g(x)) applies g first even though f is on the left. Working the other way gives a different answer nearly every time, which is why the two are worth checking against each other.

Also called composite functions, composition of functions or inverse functions.

What you can put on this worksheet

Evaluate a function at a value
Given f(x)=−3x+5, find f(2) → −1
Add and multiply functions
Given f(x)=x+3 and g(x)=−3x−3, find (f+g)(x) → −2x
Compose two functions
Given f(x)=x+3 and g(x)=−3x−3, find f(g(x)) → −3x
Find the inverse of a linear function
Find the inverse of f(x)=3x+4 → f−1(x)=x−43

Questions about these worksheets

Yes. Every function operations and inverses 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 function operations and inverses 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 4: evaluate a function at a value, add and multiply functions, compose two functions and find the inverse of a linear function. Tick as many as you want and set how many of each, or let it spread them evenly.

Doing the functions in the order they are written. f(g(x)) applies g first even though f is on the left. Working the other way gives a different answer nearly every time, which is why the two are worth checking against each other.