Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 472: 118

$f^{-1}(x)=e^{x-6}+1$, domain $(-\infty,\infty)$, rang $(1,\infty)$

Step 1. Find the inverse: $y=ln{(x-1)}+6 \longrightarrow x=e^{y-6}+1 \longrightarrow f^{-1}(x)=e^{x-6}+1$ Steo 2. For $f^{-1}(x)=e^{x-6}+1$, we can find domain $(-\infty,\infty)$, rang $(1,\infty)$