Free Printable WorksheetMathAlgebra IIMath CurriculumF-BF.4a

ALG2.81 Finding Inverses Algebraically Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.81 Finding Inverses Algebraically. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.81 Finding Inverses Algebraically - Find the inverse of a one-to-one function and restrict domain when necessary to make an inverse exist. Associated source-listed standards: CCSS F-BF.4a; CA CCSSM F-BF.4a; MA 2017 F-BF.4a; NY NGLS F-BF.4a; TX TEKS Algebra II: §111.40.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.81 Finding Inverses Algebraically skill assessments:

Problem 1Difficulty: Mastery

Which inverse matches f(x) = |x - 4| + 3 when the original domain is x <= 4?

A-x + 7, x >= 3

Bx + 1, x >= 3

Cx - 1, x >= 3

D-x + 7, x <= 3

Solution & Explanation:On the restricted domain x <= 4, the absolute value function becomes linear. Solving for the inverse gives -x + 7, x >= 3.

Problem 2Difficulty: Mastery

Two students restrict f(x) = (x - 2)² + 5. Student A uses x >= 2. Student B uses x <= 2. Which pair of inverse functions is correct?

AStudent A: 2 - sqrt(x - 5); Student B: 2 + sqrt(x - 5)

BStudent A: -2 + sqrt(x - 5); Student B: -2 - sqrt(x - 5)

CStudent A: 2 + sqrt(5 - x); Student B: 2 - sqrt(5 - x)

DStudent A: 2 + sqrt(x - 5); Student B: 2 - sqrt(x - 5)

Solution & Explanation:The restriction x >= 2 uses the right branch, so Student A gets 2 + sqrt(x - 5). The restriction x <= 2 uses the left branch, so Student B gets 2 - sqrt(x - 5).

Problem 3Difficulty: Mastery

If f^(-1)(x) = ((x - 1)/4)² + 6, x >= 1, what is f(x)?

A(x - 6)² + 1

B4sqrt(x + 6) + 1

C4sqrt(x - 6) + 1

D-4sqrt(x - 6) + 1

Solution & Explanation:Swap x and y in f^(-1)(x) = ((x - 1)/4)² + 6 and solve for y. The original function is f(x) = 4sqrt(x - 6) + 1.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard F-BF.4a (Find the inverse of a one-to-one function and restrict domain when necessary to make an inverse exist. Associated source-listed standards: CCSS F-BF.4a; CA CCSSM F-BF.4a; MA 2017 F-BF.4a; NY NGLS F-BF.4a; TX TEKS Algebra II: §111.40.).