Produce an invertible function from a non-invertible function by restricting the domain.

Common Core: HSF-BF.B.4

Ex: Restrict the Domain to Make a Function 1 to 1, Then Find the Inverse

This video explains how to restrict the domain of a function to make the function one to one. Then it explains how to determine the inverse function.

Animation: Inverse Function

Illustrates why a function must be one-to-one in order to have an inverse function.

Wolfram – Finding an Inverse

Polynomials that are strictly increasing or strictly decreasing have inverse functions.

A polynomial is one-to-one on its intervals of increase and decrease. A restriction of the polynomial is a new function, with one of those intervals as its domain, whose values agree with the values of the polynomial on that interval. Those functions are one-to-one on those intervals and have inverses.

The graphs of a function and its inverse are symmetric in the line y = x.

This Demonstration plots the graphs of each restricted function (solid curve) and its inverse (dashed curve) in matching colors.

Inverse functions with restricted domain.

Inverse Functions Restrict the Domain.

Restrict Domain and Find Inverse

Given a function that is not one-to-one, restrict the domain so that the function is one-to-one and find the inverse.

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