CCSS.Math.Content.HSF-BF.B.4a

MathGrades 9–12Building Functions

The Standard

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Common Core State Standards for Mathematics · Build new functions from existing functions

Teacher's field guide

What Students Need to Do: Students find the input that produces a given output. They reverse a simple function’s operations, write its inverse, and check the result by composition.
What Mastery Looks Like: Given f(x) = c, students isolate x and express it in terms of c. They write f⁻¹(x), include needed restrictions, and verify that both compositions return x.
Common Misconceptions: Students often read f⁻¹(x) as 1/f(x). They may swap x and y but stop before solving for y. With rational functions, they may miss excluded inputs or outputs.
How to Assess It: Exit ticket: For f(x) = (x + 1)/(x - 1), solve f(x) = c, write f⁻¹(x), and state its domain.

Lesson moves

Give groups cards showing functions, inverse rules, and input-output pairs, then have them build correct matching sets.
Ask students to explain why reversing operations requires changing both the operation and its order.
Run an inverse relay where teams solve f(x) = c, write the inverse, and check another team’s composition.
Use a Celsius-to-Fahrenheit rule, then have students find the temperature that produced a given reading and write the reverse rule.

Free download

$Preview of the CCSS.Math.Content.HSF-BF.B.4a printable worksheet$

A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-BF.B.4a, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Learning progression

If students are struggling here, check these first.

Mastery here sets students up for these next.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.