Determine [math]f(g(x))[/math] and [math]g(f(x))[/math] to verify that [math]f(x) = 2x^{3} – 1[/math] and [math]g(x)=\sqrt[3]{\frac{x+1}{2}}[/math] are inverses of each other. [i]Note[/i]: Due to functionality, this applet uses a different (but equivalent) notation for [math]g(x)[/math].
[list=1] [*]Find [math]f(g(x))[/math] using [math]f(x) = 2x^{3} – 1[/math] and [math]g(x)=\sqrt[3]{\frac{x+1}{2}}[/math]. [*]Find [math]g(f(x))[/math] using [math]f(x) = 2x^{3} – 1[/math] and [math]g(x)=\sqrt[3]{\frac{x+1}{2}}[/math]. [*]State a conclusion about whether [math]g(x)[/math] is the inverse of [math]f(x)[/math] based on the results for [math]f(g(x))[/math] and [math]g(f(x))[/math]. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCGPS Advanced Algebra[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.