Wyoming Math F.BF.4a

MathGrades 9–12Building Functions

The Standard

Find inverse functions. Write an expression for the inverse of a simple, invertible function f(x). Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions, if and only if, f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g.

2023 Wyoming Mathematics Content and Performance Standards · Build new functions from existing functions.

Teacher's field guide

What This Standard Means

What Students Need to Do: Students reverse a function's input and output to find an inverse rule. They solve for the original input and check that the rules undo each other. They check whether each output comes from only one input.
What Mastery Looks Like: Given f(x)=3x−7, a student writes f⁻¹(x)=(x+7)/3 and checks it with an input. They can explain why x² needs a restricted domain to have an inverse function.
Common Misconceptions: Students may mistake f⁻¹(x) for 1/f(x). They may swap x and y without solving for y. They may also assume x² has an inverse function on all real numbers.
How to Assess It: Exit ticket: For f(x)=3x−7, write the inverse rule and show that f⁻¹(f(4))=4.

Lesson moves

Ways to Teach It

Give students input-output cards for f(x)=2x+3; they swap each pair and write the reverse rule.
Ask why y=x² has no inverse function on all real numbers; have students use 2 and −2 in their answers.
Play inverse match: students pair rule cards such as 4x+1 and (x−1)/4, then test each pair with one input.
Hand out a weather report showing 68°F; students reverse F=9C/5+32 to find Celsius and check their result.

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