Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 472: 113

$ f^{-1}(x)=ln(x)+5$, domain $(0,\infty)$, rang $(-\infty,\infty)$

Step 1. Find the inverse: $y=e^{x-5} \longrightarrow x=ln(y)+5 \longrightarrow f^{-1}(x)=ln(x)+5$ Steo 2. For $ f^{-1}(x)=ln(x)+5$, we can find domain $(0,\infty)$, rang $(-\infty,\infty)$