Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.
Verify whether two functions are inverse functions
Problem
Verify whether \(f(x)=2x+3\) and \(g(x)=(x-3)/2\) are inverses. Compute \(f(g(x))\) and \(g(f(x))\) with substitutions shown, simplify both, and state the inverse conclusion from the identity-function test.
Big Picture
What this problem is really about
Inverse functions must undo each other in both composition orders. We’ll substitute each complete rule into the other with grouping intact, simplify the operations in their natural cancellation order, and compare both results with the identity function on the stated domains.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
