Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.
Choose a domain restriction so a quadratic has an inverse function
Problem
Use the graph of \(f(x)=x^{2}\) and restrict it to the complete right branch beginning at the vertex. State the restricted domain, explain why that branch is one-to-one using monotonicity or the horizontal-line test, and give the resulting range that becomes the inverse domain.
A parabola becomes one-to-one when its domain retains one complete monotonic branch beginning at the vertex. We’ll locate that turning point, follow the requested side of the graph, verify that horizontal lines meet the retained branch at most once, and transfer its range to the inverse domain.
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.
