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F-BF.4.a Warmup M2-017-A10-V01

Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.

Use a point on a function to write the matching fact about its inverse

Problem

The graph of \(f\) contains the point \((2,7)\). What does that tell you about the inverse function?

Prompt plots the given point without the worked conclusion. Open full size
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What this problem is really about

A point on a function records an input-output pair, and an inverse reverses the two roles. We’ll translate the plotted point into function notation, swap its coordinates as a reflection across the line y equals x, and translate the reflected point back into inverse notation.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
F-BF.4.a
Category
Functions
Domain
Building Functions
Objective
Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.
Problem type
Use a point on a function to write the matching fact about its inverse