Problem preview

F-BF.4.a Warmup M3-020-A08-V02

Find inverse functions for simple invertible functions, including rational examples.

Verify that two functions are inverse functions using composition

Problem

For \(f(x)~=~\sqrt{x~-~1}\) and \(g(x)~=~x^2~+~1\) restricted to \(x~\ge~0\), compute \(\text{both}~\text{compositions}\) and state the domain where each equals \(x\).

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f(g(x)) = |x| and g(f(x)) = x

f(g(x)) = x for x >= 0 and g(f(x)) = x for x >= 1

f(g(x)) = x for all real x and g(f(x)) = x for x >= 1

f(g(x)) = x for x >= 0

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Curriculum context

Course: Math III
Standard: F-BF.4.a
Category: Functions
Domain: Building Functions
Objective: Find inverse functions for simple invertible functions, including rational examples.
Problem type: Verify that two functions are inverse functions using composition