Question

Finding the inverse function for f(x)=1/x^2

Answer 1

to get the inverse of any expression, we start off by doing a quick switcheroo on the variables and then solve for "y".

$\stackrel{f(x)}{y}=\cfrac{1}{x^2}\implies \stackrel{\textit{quick switcheroo}}{x=\cfrac{1}{y^2}}\implies y^2=\cfrac{1}{x}\implies y=\sqrt{\cfrac{1}{x}}\implies \stackrel{f^{-1}(x)}{y}=\cfrac{1}{\sqrt{x}}$