## Calculus 8th Edition

$f^{-1}(x)=e^{\frac{x}{2}}+1$
Given: $y=2ln(x-1)$ $ln(x-1)=\frac{y}{2}$ $x-1=e^{\frac{y}{2}}$ $x=e^{\frac{y}{2}}+1$ Now, replace the terms to find out the value of inverse function. $y=e^{\frac{x}{2}}+1$ Hence, $f^{-1}(x)=e^{\frac{x}{2}}+1$