Determine [math]f(g(x))[/math] and [math]g(f(x))[/math] to verify that [math]g(x) = x^{2} – 3[/math] is the inverse of [math]f(x)= ± \sqrt{x + 3}[/math]. [i]Note[/i]: Due to functionality, this applet uses a different (but equivalent) notation for [math]f(x)[/math].
[list=1] [*]Find [math]f(g(x))[/math] using [math]f(x)= ±\sqrt{x + 3}[/math] and [math]g(x) = x^{2} – 3[/math]. [*]Find [math]g(f(x))[/math] using [math]f(x)= ±\sqrt{x + 3}[/math] and [math]g(x) = x^{2} – 3[/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.