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] [*]Determine if the function is one-to-one. [*]Rewrite the function [math]f(x)[/math] in the form “[math]y =[/math].” [*]Switch [math]x[/math] and [math]y[/math] in the original equation of the function. [*]Solve the new equation for [math]y[/math] by using inverse operations. [*]Replace [math]y[/math] with [math]f^{–1}(x)[/math] to show that the equation is the inverse of [math]f(x)[/math]. [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math II[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.

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

[list=1] [*]Determine if the function is one-to-one. [*]Determine a restricted domain for [math]f(x)[/math] on which the function is one-to-one. [*]Rewrite the function [math]f(x)[/math] in the form “[math]y =[/math].” [*]Switch [math]x[/math] and [math]y[/math] in the original equation of the function. [*]Solve the new equation for [math]y[/math] by using inverse operations. [*]Replace [math]y[/math] with [math]f^{–1}(x)[/math] to show that the equation is the inverse of [math]f(x)[/math]. [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math II[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.