How do you find inverse for certain exponential function?

Question

How do you find inverse for $y=\frac{e^x-e^{-x}}{2}$?

Answer 1

Let $f(x)=y=\dfrac{e^x-e^{-x}}2=\dfrac{e^{2x}-1}{2e^x}$

$\implies e^{2x}-2e^x y-1=0\implies e^x=\cdots\implies x=\ln(\cdots)$

$\implies f^{-1}(y)=x=\cdots$