AHSME 1967 Problem 14

Let $f(t)=\frac{t}{1-t}$, $t \not= 1$. If $y=f(x)$, then $x$ can be expressed as $\textbf{(A)}\ f\left(\frac{1}{y}\right) \textbf{(B)}\ -f(y) \textbf{(C)}\ -f(-y) \textbf{(D)}\ f(-y) \textbf{(E)}\ f(y)$