Find the inverse, [math]g(x)[/math], of the function [math]f(x) = 4x^2[/math] and determine the domain value(s) over which the inverse exists.

[list=1][br][*]Switch the domain and function variables, and then rename [math]f(x)[/math] as [math]g(x)[/math].[br][/*][*]Solve the possible inverse for [math]g(x)[/math].[br][/*][*]Determine the domain of [math]g(x)[/math].[br][/*][*]Determine the range of [math]g(x)[/math].[br][/*][*]Determine the domain of [math]f(x)[/math].[br][/*][*]Determine whether the function [math]f(x)[/math] exhibits one-to-one correspondence.[br][/*][*]Determine the parts of its domain over which [math]f(x)[/math] exhibits one-to-one correspondence.[br][/*][*]Determine the range of [math]f(x)[/math].[br][/*][*]Match domains to ranges to find the inverse(s) of [math]f(x)[/math].[br][/*][/list][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com/]www.walch.com[/url] for more information.