Indicate whether sech(x) is invertible for [0, infinity) and explain why.
The Attempt at a Solution
Sooo... I know that:
sech(x) = 2 / ( ex + e-x )
I know that to get the inverse equation I'd need to swap the y and the x... but I'm trying to show whether it's invertible so I don't know how much that would do me. I think I need to prove that the equation is monotonic, ie the derivative should be > 0 ). Hence, I took the derivative of the equation to be:
y' = - 2 (ex - e-x) / (ex + e-x)2
Is that right? If so, is that enough to answer the question?