CCSS.Math.Content.HSF-BF.B.4
The Standard
Find inverse functions.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students reverse a function by exchanging its inputs and outputs, then solve for the new output. They check the result through composition and restrict domains when needed.
What Mastery Looks Like
- Students can find an inverse from an equation, table, or graph. They can verify it using composition and explain when a domain restriction is needed.
Common Misconceptions
- Students often confuse an inverse function with the reciprocal 1/f(x). They may swap x and y but not solve for y, or ignore the need to restrict a domain.
How to Assess It
- Exit ticket: For f(x) = (x − 2)² with x ≥ 2, find the inverse, state its domain, and verify one composition.
Lesson moves
Ways to Teach It
Give pairs of input and output cards, then have students reverse each pair and build the inverse table and graph.
Ask students to explain why f(x) = x² needs a restricted domain before its inverse can be a function.
Run a matching game with function equations, inverse equations, graphs, and composition checks.
Use a temperature conversion formula, then have students reverse it to convert temperatures back to the original scale.
Free download
Printable HSF-BF.B.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-BF.B.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSF-IF.A.1
Finding inverses requires knowing functions as input-output rules, using f(x) notation, and tracking domain and range reversal.
- CCSS.Math.Content.HSF-IF.A.2
Inverse functions require tracking inputs and outputs in function notation, especially interpreting f(a)=b as f^{-1}(b)=a.
- CCSS.Math.Content.HSA-CED.A.4
Solving for a chosen variable carries over directly when finding an inverse by switching input and output and isolating the new output.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSF-BF.B.4d
Restricting a domain to make a function invertible requires knowing what inverses are and when a function has one.
- CCSS.Math.Content.HSF-BF.B.5
Finding inverse functions carries over to seeing logarithms as the inverse of exponential functions and using that relationship to solve equations.
Keep exploring
Related Standards
- CCSS.Math.Content.HSF-BF.B.4a
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.
- CCSS.Math.Content.HSF-BF.B.4c
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
- CCSS.Math.Content.HSF-BF.B.4b
(+) Verify by composition that one function is the inverse of another.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.