Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 472: 115

$f^{-1}(x)=ln(x+4)-1$, domain $(-4,\infty)$, rang $(-\infty,\infty)$

Step 1. Find the inverse: $y=e^{x+1}-4 \longrightarrow x=ln(y+4)-1 \longrightarrow f^{-1}(x)=ln(x+4)-1$ Steo 2. For $f^{-1}(x)=ln(x+4)-1$, we can find domain $(-4,\infty)$, rang $(-\infty,\infty)$