Question

Which of the following is the inverse of the function y=lnx9?

Answer 1

Given

$y=lnx^9$

We can find the inverse below.

Explanation

$\begin{gathered} y=lnx^9 \\ swap\text{ x and y} \\ x=lny^9 \\ therefore; \\ x=9lny \\ lny=\frac{x}{9} \\ e^{lny}=\frac{x}{9} \\ y=e^{\frac{x}{9}}\Rightarrow y^{-1}=e^{\frac{x}{9}} \end{gathered}$

Answer: Option D