How do you find the inverse of f(x) = e^x - e^-xf(x)=ex−e−x?
1 Answer
Jan 30, 2016
Let
f^(-1)(y) = ln((y+sqrt(y^2+4))/2)f−1(y)=ln(y+√y2+42)
Explanation:
Let
Then
So
Using the quadratic formula we find:
e^x = (y+-sqrt(y^2+4))/2ex=y±√y2+42
One of these roots is negative, requiring
So only the positive root is useful for
x = ln((y+sqrt(y^2+4))/2)x=ln(y+√y2+42)
That is:
f^(-1)(y) = ln((y+sqrt(y^2+4))/2)f−1(y)=ln(y+√y2+42)