I am stuck with this problem,
A function $f(x)$ is defined as $f(x) = \sinh(x)$. Another function $g(x)$ is such that $f(g(x)) = x$.
Find the value of $\large g(\frac{e^{2012}-1}{2e^{1006}})$
I tried representing $f(x) =\large \frac{e^{2x}-1}{2e^{x}}$,and then using some algebraic manipulation but I am unable to get the correct answer. Any ideas?