Worksheets · Precalculus

Inverse functions worksheet for Precalculus

Precalculus pushes inverses past lines to cubes, cube roots and square roots, checks whether two functions are inverses by composing them, and graphs a function with its inverse as a mirror image across y = x.

Also taught in Algebra 2 and Algebra 1, each at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse Functions

Date Period

Find each inverse, or answer as asked.

  1. Find the inverse

    Find the inverse of f(x)=42x+45
  2. Find the inverse of f(x)=3x3+4
  3. Find the inverse of f(x)=−51x−7
  4. Find the inverse of f(x)=(x+6)3+1
  5. Find the inverse of f(x)=−56x+55
  6. Find the inverse of f(x)=x−2
  7. Find the inverse of f(x)=29x−37
  8. Find the inverse of f(x)=(x+5)3−1
  9. Find the inverse of f(x)=−33x−4
  10. Find the inverse of f(x)=(x−2)3−6

  1. Decide whether the functions are inverses

    Are f(x)=4x−3 and g(x)=x−34 inverses?
  2. Are f(x)=−4x−1 and g(x)=−x4+1 inverses?
  3. Are f(x)=2x−3 and g(x)=x+32 inverses?
  4. Are f(x)=5x+5 and g(x)=x−55 inverses?
  5. Are f(x)=3x+1 and g(x)=x3−1 inverses?

  1. Graph a function and its inverse

    Graph f(x)=2x+2 and its inverse on the same grid.−10−10−5−5551010
  2. Graph f(x)=−12x−3 and its inverse on the same grid.−10−10−5−5551010
  3. Graph f(x)=2x−4 and its inverse on the same grid.−10−10−5−5551010
  4. Graph f(x)=−12x+4 and its inverse on the same grid.−10−10−5−5551010
  5. Graph f(x)=13x and its inverse on the same grid.−10−10−5−5551010

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse FunctionsAnswer keyVersion 2

Date Period

Find each inverse, or answer as asked.

  1. Find the inverse

    Find the inverse of f(x)=42x+45f−1(x)=x−4542
  2. Find the inverse of f(x)=3x3+4f−1(x)=x−433
  3. Find the inverse of f(x)=−51x−7f−1(x)=−x−751
  4. Find the inverse of f(x)=(x+6)3+1f−1(x)=x−13−6
  5. Find the inverse of f(x)=−56x+55f−1(x)=−x+5556
  6. Find the inverse of f(x)=x−2f−1(x)=x2+2, x≥0
  7. Find the inverse of f(x)=29x−37f−1(x)=x+3729
  8. Find the inverse of f(x)=(x+5)3−1f−1(x)=x+13−5
  9. Find the inverse of f(x)=−33x−4f−1(x)=−x−433
  10. Find the inverse of f(x)=(x−2)3−6f−1(x)=x+63+2

  1. Decide whether the functions are inverses

    Are f(x)=4x−3 and g(x)=x−34 inverses?No
  2. Are f(x)=−4x−1 and g(x)=−x4+1 inverses?No
  3. Are f(x)=2x−3 and g(x)=x+32 inverses?Yes
  4. Are f(x)=5x+5 and g(x)=x−55 inverses?Yes
  5. Are f(x)=3x+1 and g(x)=x3−1 inverses?No

  1. Graph a function and its inverse

    Graph f(x)=2x+2 and its inverse on the same grid.−10−10−5−5551010ff−1y = xf−1(x)=12x−1, the mirror image of f across y=x
  2. Graph f(x)=−12x−3 and its inverse on the same grid.−10−10551010ff−1y = x−5−5f−1(x)=−2x−6, the mirror image of f across y=x
  3. Graph f(x)=2x−4 and its inverse on the same grid.−10−10551010ff−1y = x−5−5f−1(x)=12x+2, the mirror image of f across y=x
  4. Graph f(x)=−12x+4 and its inverse on the same grid.−10−10−5−555ff−1y = x1010f−1(x)=−2x+8, the mirror image of f across y=x
  5. Graph f(x)=13x and its inverse on the same grid.−10−10−5−5551010ff−1y = xf−1(x)=3x, the mirror image of f across y=x

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

How to do these

Find the inverse of f(x)=3x3−5

  1. Swap: x = 3y³ - 5.
  2. Add 5, then divide by 3: y³ = (x + 5)/3.
  3. Take the cube root.

The answer is f−1(x)=x+533.

Where students go wrong

Undoing the steps in the wrong order. In 3x³ - 5 the last step was subtracting 5, so add 5 first, then divide by 3, and take the cube root last.

Also called finding the inverse or f inverse of x.

What you can put on this worksheet

Find the inverse of a linear function
Find the inverse of f(x)=3x+4 → f−1(x)=x−43
The inverse of a quadratic on a restricted domain
Find the inverse of f(x)=x2+1, x≥0 → f−1(x)=x−1
The inverse of a rational function
Find the inverse of f(x)=x+6x+1 → f−1(x)=x−6−x+1
Is it one-to-one
Is it one-to-one? f(x)=x2+4 → No
Are they inverses?
Are f(x)=4x+4 and g(x)=x−44 inverses? → Yes
Cubics, cube roots and square roots
Find the inverse of f(x)=x−53−5 → f−1(x)=(x+5)3+5
Graph a function and its inverse
Graph f(x)=−12x−4 and its inverse on the same grid. → f−1(x)=−2x−8, the mirror image of f across y=x
Check whether two functions are inverses
Are f(n)=3(n−1)3 and g(n)=4+9n33 inverses? → No
Graph a function with its inverse
Find the inverse and graph both: f(x)=x3+2 → f−1(x)=x−23
Are they inverses? (fractions)
Are these inverses? Find f(g(x)). f(x)=65x−1, g(x)=56x+116 → No; f(g(x))=x+65
Inverse of a line with fractions
Find the inverse:
f(x)=65x−1 → f−1(x)=56x+56
Fourth and fifth roots
Find the inverse:
f(x)=x+55−5 → f−1(x)=(x+5)5−5

Questions about these worksheets

Yes. Every inverse 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.

Precalculus is usually taken around 11th or 12th 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 inverse 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 12: find the inverse of a linear function, the inverse of a quadratic on a restricted domain, the inverse of a rational function, is it one-to-one, are they inverses?, cubics, cube roots and square roots, graph a function and its inverse, check whether two functions are inverses, graph a function with its inverse, are they inverses? (fractions), inverse of a line with fractions and fourth and fifth roots. Tick as many as you want and set how many of each, or let it spread them evenly.

Undoing only one of the two operations. The inverse has to reverse both, in the opposite order: subtract the 4 first, then divide by the 2.