Worksheets · Precalculus

Solving f(x) = k worksheet for Precalculus

Precalculus sets f(x) = k for nonlinear functions as well as lines, including absolute values and quadratics that can return two inputs for one output. It is the same question as where the horizontal line y = k meets the graph, so expect answer sets with more than one value.

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

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

Sigma Prep · sigmaprep.io/worksheets

Name

Solving for an Input

Date Period

Solve each equation.

  1. Find the input that gives an output

    Given f(x)=2x−5, solve f(x)=7
  2. Given f(x)=x2+5, solve f(x)=21
  3. Given f(x)=−12x−20, solve f(x)=−212
  4. Given f(x)=x2−3, solve f(x)=46
  5. Given f(x)=6x+11, solve f(x)=71
  6. Given f(x)=∣x+2∣, solve f(x)=7
  7. Given f(x)=−5x+4, solve f(x)=44
  8. Given f(x)=∣x−2∣, solve f(x)=1
  9. Given f(x)=10x+17, solve f(x)=−133
  10. Given f(x)=x2−5, solve f(x)=−4
  11. Given f(x)=−8x−12, solve f(x)=84
  12. Given f(x)=x, solve f(x)=6
  13. Given f(x)=3x−5, solve f(x)=−11
  14. Given f(x)=∣x+4∣, solve f(x)=4
  15. Given f(x)=−11x+25, solve f(x)=−118
  16. Given f(x)=x2+8, solve f(x)=89
  17. Given f(x)=−6x−13, solve f(x)=−67
  18. Given f(x)=x−1, solve f(x)=2
  19. Given f(x)=−x+2, solve f(x)=−2
  20. Given f(x)=∣x−6∣, solve f(x)=4

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

Sigma Prep · sigmaprep.io/worksheets

Name

Solving for an InputAnswer keyVersion 2

Date Period

Solve each equation.

  1. Find the input that gives an output

    Given f(x)=2x−5, solve f(x)=7{6}
  2. Given f(x)=x2+5, solve f(x)=21{−4,4}
  3. Given f(x)=−12x−20, solve f(x)=−212{16}
  4. Given f(x)=x2−3, solve f(x)=46{−7,7}
  5. Given f(x)=6x+11, solve f(x)=71{10}
  6. Given f(x)=∣x+2∣, solve f(x)=7{−9,5}
  7. Given f(x)=−5x+4, solve f(x)=44{−8}
  8. Given f(x)=∣x−2∣, solve f(x)=1{1,3}
  9. Given f(x)=10x+17, solve f(x)=−133{−15}
  10. Given f(x)=x2−5, solve f(x)=−4{−1,1}
  11. Given f(x)=−8x−12, solve f(x)=84{−12}
  12. Given f(x)=x, solve f(x)=6{36}
  13. Given f(x)=3x−5, solve f(x)=−11{−2}
  14. Given f(x)=∣x+4∣, solve f(x)=4{−8,0}
  15. Given f(x)=−11x+25, solve f(x)=−118{13}
  16. Given f(x)=x2+8, solve f(x)=89{−9,9}
  17. Given f(x)=−6x−13, solve f(x)=−67{9}
  18. Given f(x)=x−1, solve f(x)=2{5}
  19. Given f(x)=−x+2, solve f(x)=−2{4}
  20. Given f(x)=∣x−6∣, solve f(x)=4{2,10}

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

How to do these

f(x)=x2−4x. Solve f(x)=12

  1. Write it out: x² - 4x = 12, so x² - 4x - 12 = 0.
  2. Factor: (x - 6)(x + 2) = 0.

The answer is {−2,6}.

Where students go wrong

Stopping at one input. A quadratic or absolute value can reach the same output twice, so f(x) = 12 here has two answers, -2 and 6.

Also called solving function equations or finding x given f(x).

What you can put on this worksheet

Find the input that gives an output
Given f(x)=3x+1, solve f(x)=−14 → {−5}
A nonlinear f(x) = k
Given f(x)=x2+4, solve f(x)=40 → {−6,6}

Questions about these worksheets

Yes. Every solving f(x) = k 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 solving f(x) = k 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: find the input that gives an output and a nonlinear f(x) = k. Tick as many as you want and set how many of each, or let it spread them evenly.

Substituting the number for x rather than for f(x). f(x) = 8 means the output is 8, so the 8 goes on the right of the equation, not into the rule.