what is the correct inverse function for f(x)=In(3x)

Answer:[tex]f^{-1}(x)=\dfrac{e^x}{3},\ x\in(-\infty,\infty),\ y>0[/tex]Step-by-step explanation:Consider the function [tex]f(x)=\ln 3x.[/tex] the domain of this function is x>0 and the range of this function is all real numbers. The inverse function has the domain all real numbers and the range y>0.If [tex]y=\ln 3x,[/tex]then[tex]3x=e^y,\\ \\x=\dfrac{e^{y}}{3}.[/tex]Change x into y and y into x:[tex]y=\dfrac{e^x}{3}.[/tex]Thus, the inverse function is [tex]f^{-1}(x)=\dfrac{e^x}{3}.[/tex]