Grade 11 · Math · Algebra 2

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

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

Grade 11 Math Worksheet - Challenge Me

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1.
On a worksheet, f(x) = (x + 2)² − 5 for x ≥ -2. Pia finds the inverse, with domain x ≥ -5. What is f⁻¹(x)?
- 1/((x + 2)² − 5)
- √(x − 2) + 5
- √(x + 5) − 2
- -√(x + 5) − 2
- √(x − 5) + 2
2.
In a notebook, Ren inverts f(x) = (x − 5)² + 1, kept to x ≥ 5. What is f⁻¹(x) for x ≥ 1?
- -√(x − 1) + 5
- 1/((x − 5)² + 1)
- √(x + 1) − 5
- √(x − 1) + 5
- √(x + 5) − 1
3.
Tala works in pencil with f(x) = (x − 1)² + 3 for x ≤ 1. Which rule is f⁻¹(x)?
- -1 − √(x + 3)
- 1 + √(x − 3)
- 1 − √(x − 3)
- 1/((x − 1)² + 3)
- -√(x + 1) − 3
4.
On a puzzle card, f(x) = (x + 4)² − 2 for x ≤ -4. Zee needs the rule for f⁻¹(x). What is it?
- -4 − √(x + 2)
- -√(x − 4) + 2
- -4 + √(x + 2)
- 4 − √(x − 2)
- 1/((x + 4)² − 2)
5.
On a worksheet, f(x) = 3/(x − 2). Ari swaps x and y and solves for y. What is f⁻¹(x)?
- 3/y + 2
- 3/(x + 2)
- (x − 2)/3
- 3/x − 2
- 3/x + 2
6.
Esme works in pencil to invert f(x) = 2/(x + 3). Which rule is f⁻¹(x)?
- 2/x + 3
- (x + 3)/2
- 2/(x − 3)
- 2/x − 3
- 2/y − 3
7.
On a puzzle card, f(x) = 6/x − 2. Jun needs f⁻¹(x). What is it?
- 6/x + 2
- 6/(y + 2)
- 6/(x − 2)
- x/(-2x + 6)
- 6/(x + 2)
On a worksheet, f(x) = 2x + 6 and g(x) = (1/2)x − 3. Kira composes them to test whether g is f⁻¹. What is f(g(x))?
In a notebook, Luz has f(x) = 3x − 4 and g(x) = (1/3)x + 4. What is f(g(x)), with like terms combined?
Milo checks in pencil whether g(x) = (1/4)x + 3/4 undoes f(x) = 4x − 3. What is f(g(x))?

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.

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