Find the inverse, [math]f^{–1}(x)[/math], of the function [math]f(x) = x(x – 1)[/math] and determine the domain and range value(s) over which the inverse exists.
[list=1] [*]Determine whether an inverse exists for this function. [*]Determine the range of [math]f(x)[/math]. [*]Calculate the inverse by switching the domain and function variables, and then renaming [math]f(x)[/math] as [math]f^{–1}(x)[/math]. [*]Rewrite the inverse in a form that can be solved for [math]f^{–1}(x)[/math]. [*]Solve for [math]f^{–1}(x)[/math] using the quadratic formula. [*]Determine the domain of [math]f^{–1}(x)[/math]. [*]Determine the range of [math]f^{–1}(x)[/math]. [*]Summarize your conclusions. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCSS Integrated Pathway: Mathematics III[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.