Question

What is the inverse of the function below?

Answer 1

`f^(-1)(x)=ln(x)`

Explanation:

Given function is
`f\left(x\right)=e^x`.

Now we need to find it's inverse so follow these steps:

Step 1: replace f(x) with y.

`y=e^x`

Step 2: Switch x and y.

`x=e^y`

Step 3: Solve for y.

`x=e^y`

`ln(x)=ln(e^y)`

`ln(x)=y`

`y=ln(x)`

Step 4: Replace y with
`f^(-1)(x)`.

`f^(-1)(x)=ln(x)`

Hence final answer is
`f^(-1)(x)=ln(x)`.

Answer 2

`{f}^( - 1)(x) = ln(x)`

EXPLANATION

The given function is

`f(x) = {e}^(x)`

Let

`y={e}^(x)`

We interchange x and y.

`x={e}^(y)`

Solve for y.

`y = ln(x)`

This implies that,

`{f}^( - 1)(x) = ln(x)`

The correct answer is C