Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 472: 117

$f^{-1}(x)=\frac{1}{3}e^{x/2}$, domain $(-\infty,\infty)$, rang $(0,\infty)$

Step 1. Find the inverse: $y=2ln{3x} \longrightarrow x=\frac{1}{3}e^{y/2} \longrightarrow f^{-1}(x)=\frac{1}{3}e^{x/2}$ Steo 2. For $f^{-1}(x)=\frac{1}{3}e^{x/2}$, we can find domain $(-\infty,\infty)$, rang $(0,\infty)$