Problem preview

F-BF.4.a Warmup M2-017-A05-V03

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

Verify whether two functions are inverse functions

Problem

Determine whether \(f(x)=x+5\) and \(g(x)=x-4\) are inverses by evaluating both composition orders. Simplify each result, compare it with \(x\), and explain what the \(\text{one}\text{-}\text{unit}\) mismatch shows about the proposed inverse.

Answer choices

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Yes. Both compositions equal x+1, so the functions undo each other.

Yes. f(g(x))=x and g(f(x))=x.

No. f(g(x))=x−1 and g(f(x))=x−1.

No. f(g(x))=x+1 and g(f(x))=x+1, so neither composition is x.

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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: Verify whether two functions are inverse functions