Problem preview
F-BF.4.a Warmup M2-017-A06-V01

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

Determine whether a function has an inverse on a stated domain

Problem

Determine whether \(f(x)=x^2\) has an inverse function when its domain is all real numbers.

Big Picture

What this problem is really about

Whether an inverse relation is a function depends on one-to-one behavior over the exact domain that was given. We’ll look for two allowed inputs with the same output, connect that counterexample to a horizontal line crossing the graph more than once, and then interpret what coordinate reversal would do.

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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
Determine whether a function has an inverse on a stated domain