Question

What is the inverse of the function below?

Answer 1

Answer:

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

Step-by-step 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

ANSWER

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

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