Question

What is the correct inverse function for f(x) = /n5x?

Answer 1

The given function is

`f(x)=\ln 5x`

It is important to know that the inverse function for logarithms is exponential functions. In this case, we change f(x) to y.

`y=\ln 5x`

Then, we isolate x

`\begin{gathered} e^y=e^(\ln 5x) \\ e^y=5x \\ x=(e^y)/(5) \end{gathered}`

At last, we change the variables.

`y=(e^x)/(5)`

The inverse function notation is

`f^(-1)(x)=(e^x)/(5)^{}`

Hence, the answer is B.