Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-IF.1-6,9

Pre CAL.10 Inverse Functions and One to One Relationships Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.10 Inverse Functions and One to One Relationships. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.10 Inverse Functions and One-to-One Relationships - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a function and its candidate inverse (or a graph), determine whether they are inverses and select the correct inverse or justification, including any needed domain restrictions. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. Use this prompt-provided wording as the supporting standard description for this workflow.

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

Pre-Calculus

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 Pre CAL.10 Inverse Functions and One to One Relationships skill assessments:

Problem 1Difficulty: Mastery
Find the inverse of f(x) = sqrt(x + 2) - 3.
Af-1(x) = (x + 3)2 - 2, domain x >= -3
Bf-1(x) = (x - 3)2 + 2, domain x >= 3
Cf-1(x) = sqrt(x - 2) + 3, domain x >= 2
Df-1(x) = (x + 2)2 - 3, domain all real numbers
Solution & Explanation:Add 3 and square: (y + 3)2 = x + 2. Then x = (y + 3)2 - 2. The original range is y >= -3, so the inverse domain is x >= -3.
Problem 2Difficulty: Mastery
For f(x) = (x - 2)2 + 5, which domain restriction gives inverse g(x) = 2 - sqrt(x - 5)?
Ax <= 2
Bx >= 2
Call real numbers
Dx >= 5
Solution & Explanation:The inverse with a minus sign comes from the left branch of the parabola, where original inputs satisfy x <= 2.
Problem 3Difficulty: Mastery
The functions f(x) = 2x3 - 1 and g(x) = cube root of ((x + 1)/2) are inverses.
ATrue
BFalse
Solution & Explanation:Solving y = 2x3 - 1 gives x3 = (y + 1)/2, so x = cube root of ((y + 1)/2). That matches g.

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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 Pre-Calculus Math students. It aligns with educational standard HSF-IF.1-6,9 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a function and its candidate inverse (or a graph), determine whether they are inverses and select the correct inverse or justification, including any needed domain restrictions. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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