AHSME 1974 Problem 12

If $g(x)=1-x^2$ and $f(g(x))=\frac{1-x^2}{x^2}$ when $x\not=0$, then $f(1/2)$ equals $\mathrm{(A)\ } 3/4 \mathrm{(B) \ }1 \mathrm{(C) \ } 3 \mathrm{(D) \ } \sqrt{2}/2 \mathrm{(E) \ }\sqrt{2}$