Free Printable WorksheetMathAlgebra IIMath CurriculumF-BF.4a

ALG2.80 Inverse Functions and Verification Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.80 Inverse Functions and Verification. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.80 Inverse Functions and Verification - Identify whether two functions are inverses and verify inverses using composition and/or graph symmetry. 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 ALG2.80 Inverse Functions and Verification skill assessments:

Problem 1Difficulty: Mastery

Which combination of evidence is enough to conclude two functions are inverses?

AOne composition simplifies to x

BA few points look swapped, but no compositions are checked

CBoth compositions simplify to x on the allowed domains, and corresponding points reflect across y = x

DThe functions have the same y-intercept

Solution & Explanation:The strongest verification uses both algebra and graph meaning: each composition must return x, and the graphs should reflect across y = x.

Problem 2Difficulty: Mastery

Let h(x) = (2x + 1)/(x - 3). Which statement about h^-1 is correct?

Ah^-1(x) = (3x + 1)/(x - 2), and if h(5) = 11/2 then h^-1(11/2) = 5

Bh^-1(x) = (x - 3)/(2x + 1), and h^-1(11/2) = 2

Ch^-1(x) = (3x - 1)/(x + 2), and h^-1(11/2) = 5

Dh has no inverse because it is rational

Solution & Explanation:Solving y = (2x + 1)/(x - 3) gives h^-1(x) = (3x + 1)/(x - 2). Also h(5) = (10 + 1)/2 = 11/2, so the inverse must send 11/2 back to 5.

Problem 3Difficulty: Mastery

For f(x) = sqrt(x + 4) - 1, which table could represent f^-1 using the sample inputs x = -4, 0, and 5 on f?

Ax: -1, 1, 2; y: -4, 0, 5

Bx: -4, 0, 5; y: -1, 1, 2

Cx: -1, 1, 2; y: 4, 0, -5

Dx: 0, 1, 5; y: -1, 1, 2

Solution & Explanation:For f, the sample outputs are -1, 1, and 2. Swapping coordinates gives inverse points (-1, -4), (1, 0), and (2, 5), which match the first table.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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Yes! In addition to this printable worksheet, students can practice ALG2.80 Inverse Functions and Verification interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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 (Identify whether two functions are inverses and verify inverses using composition and/or graph symmetry. 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.).