Lana is driving home from her friend’s house. She is driving at a steady speed, and her distance from her home, in miles, can be represented by the function [math]f(x) = –40x + 15[/math], where [math]x[/math] is her driving time in hours. Find the inverse function [math]f^{–1}(x)[/math] to show when, in hours, Lana will be [math]x[/math] miles from home.

[list=1][br][*]Determine if the function is one-to-one.[br][/*][*]Rewrite the function [math]f(x)[/math] in the form “[math]y =[/math].”[br][/*][*]Switch [math]x[/math] and [math]y[/math] in the original equation of the function.[br][/*][*]Solve the new equation for [math]y[/math] by using inverse operations.[br][/*][*]Replace [math]y[/math] with [math]f^{–1}(x)[/math] to show that the equation is the inverse 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.

Find the inverse function of [math]f(x) = 4x^2[/math]. Use a restricted domain so the inverse is a function.

[list=1][br][*]Determine if the function is one-to-one.[br][/*][*]Determine a restricted domain for [math]f(x)[/math] on which the function is one-to-one.[br][/*][*]Rewrite the function [math]f(x)[/math] in the form “[math]y =[/math].”[br][/*][*]Switch [math]x[/math] and [math]y[/math] in the original equation of the function.[br][/*][*]Solve the new equation for [math]y[/math] by using inverse operations.[br][/*][*]Replace [math]y[/math] with [math]f^{–1}(x)[/math] to show that the equation is the inverse 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.