Question

What is the inverse of the function f(x) =(1/6x)^3?

Answer 1

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

`\stackrel{f(x)}{y}~~ = ~~\left( \cfrac{x}{6} \right)^3\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\left( \cfrac{y}{6} \right)^3} \\\\\\ \sqrt[3]{x}=\cfrac{y}{6}\implies 6\sqrt[3]{x}=y=f^(-1)(x)`