Consider the functions: \(f(x)=2 x^2\) and \(g(x)=\left(\frac{1}{2}\right)^x\)

(a) Restrict the domain of \(f\) in one specific way so that the inverse of \(f\) will also be a function.

(b) Hence draw the graph of your new function \(f\) and its inverse function \(f^{-1}\) on the same set of axes.

(c) Write the inverse of \(g\) in the form \(g^{-1}(x)=\ldots \ldots .\).

(d) Sketch the graph of \(g^{-1}\).

(e) Determine graphically the values of \(x\) for which \(\log _{\frac{1}{2}} x<0\)