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

1 Answer
Jan 23, 2016

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.