How do you find the inverse of f(x) = e^x - e^-x?
1 Answer
Jan 30, 2016
Let
f^(-1)(y) = ln((y+sqrt(y^2+4))/2)
Explanation:
Let
Then
So
Using the quadratic formula we find:
e^x = (y+-sqrt(y^2+4))/2
One of these roots is negative, requiring
So only the positive root is useful for
x = ln((y+sqrt(y^2+4))/2)
That is:
f^(-1)(y) = ln((y+sqrt(y^2+4))/2)