Question

How do you find the inverse of `f(x)=e^x-1`?

Answer 1

`f^-1(x)=log_e(x+1)`

Explanation:

Firstly, I'll assume you know that if `f(x)=y` then `f^-1(y)=x`

So now, `f(x)=e^x-1`
Rearranging the equation, and taking `y=f(x)` we get `y+1=e^x`
Applying log of base `e` on both sides `log_e(y+1)=x`
Now, given above that `f^-1(y)=x`
So this means, `f^-1(y)=log_e(y+1)`

Replacing `y` as `x` you'll get the answer.