[tex]y=f(x) =12\sqrt x\\\\\text{Replace x with y and then solve for y:}\\ \\~~~~~~~x = 12\sqrt y\\\\\implies \sqrt y = \dfrac{x}{12}\\ \\\implies y = \dfrac{x^2}{144}\\\\\implies f^{-1} (x) = \dfrac{x^2}{144} \\\\\text{Hence the inverse of the function is}~ \dfrac{x^2}{144}[/tex]
