find the inverse of Ln(2x+1)

y = ln(2x+1) \\
e^y = e^{ln(2x+1)} \\
e^y = 2x+1 \\
e^y - 1 = 2x \\
\frac{e^y - 1}{2} = x \\
f^{-1} = \frac{e^x - 1}{2}