Grade 11 · Math · Algebra 2

11th grade Find the inverse of a function, restrict the domain, and check by composition worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Find the inverse of a function, restrict the domain, and check by composition

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

In a notebook, Ren has f(x) = 4x − 8, which multiplies by 4, then subtracts 8. Type one x-term and one number. What is f⁻¹(x)?
Tala works in pencil: f(x) = 2x + 10 multiplies by 2, then adds 10. Write the inverse with one x-term and one number. What is f⁻¹(x)?
On a puzzle card, f(x) = 5x − 15; f multiplies by 5, then subtracts 15. Zee needs f⁻¹(x) as one x-term and one number. What is it?
On a worksheet, f(x) = x² + 3 for x ≥ 0. Ari wants the input that gives 52. What is f⁻¹(52)?
In a notebook, Bo has f(x) = x² − 5, with x ≥ 0. What is f⁻¹(76)?
Esme works in pencil with f(x) = (x − 2)² for x ≥ 2. What is f⁻¹(25)?
On a puzzle card, f(x) = (x + 3)² for x ≥ -3. Jun needs f⁻¹(64). What is it?
On a worksheet, f(x) = 3x − 4 and g(x) = (x + 4)/3. Kira tests whether g undoes f, starting with x = 5. What is g(f(5))?
In a notebook, Luz checks f(x) = 2x + 7 against g(x) = x/2 − 7 at x = 3. What is g(f(3))?
On a puzzle card, f(x) = 5x − 2 and g(x) = x/5 + 2. Noah checks one input, 4. What is g(f(4))?

11th grade Find the inverse of a function, restrict the domain, and check by composition worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Find the inverse of a function, restrict the domain, and check by composition. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the inverse of a linear rule by swapping x and y and solving.
I can restrict a parabola to one half so that it has an inverse, and find that inverse.
I can check whether two functions are inverses by working out f(g(x)).

Standard: F-BF.B.4a, F-BF.B.4b (+), F-BF.B.4d (+)

Words to know

swap x and y: Write y = f(x), then trade the letters to start finding f⁻¹.

restrict the domain: Keep only some inputs, such as one half of a parabola.

turning point: Where a parabola turns around: its lowest or highest point.

check by composition: f(g(x)) = x means g undoes f.

Common mistakes

Your child undid the steps of f in the same order instead of the reverse order. Try: list the steps of f, then undo them from last to first.

Your child wrote 1 over f(x) for the inverse. The small -1 means "undo f", not a reciprocal.

Your child solved for x but did not swap x and y, so the answer is in the wrong letter.

What to say

Ask: does f⁻¹ undo f, or flip it?

Ask: which letter is the input of f⁻¹?

Questions parents ask

What is the most common mistake with find the inverse of a function, restrict the domain, and check by composition?

Your child undid the steps of f in the same order instead of the reverse order. Try: list the steps of f, then undo them from last to first.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

See all Algebra 2

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records