For a suitably chosen real constant a, let a function, f: R -{- a } → R be defined by f(x)=(a -x)/(a +x). Further suppose that for any real number x…

For a suitably chosen real constant a, let a function, $\displaystyle f: \mathbf{R}-\{-\mathbf{a}\} \rightarrow \mathbf{R}$ be defined by $\displaystyle f(x)=\frac{\mathrm{a}-x}{\mathrm{a}+x}$. Further suppose that for any real number $\displaystyle x \neq-a$ and $\displaystyle f(x) \neq-a$, $\displaystyle (f \circ f)(x)=x$. Then $\displaystyle f\left(-\frac{1}{2}\right)$ is equal to :