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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 $\log _{\frac{1}{2}} x<0$
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