View Single Post
Feb15-11, 07:02 PM
P: 36
We have a formula for the derivative of an inverse function:
dy/dx = 1/(dx/dy).

Just how useful is it?
Say we want to find the inverse of a complicated function, f(x), on an interval (a,b) on which f(x) is one-to-one. Can we use integration to find such a function?

Example: Say we didn't know much about the function h(x) = sin(x), but wanted to express its inverse as an integral (this was my inspiration for the idea). How could this be done?

More importantly, this would apply to functions like F(x) = x*e^x. Its inverse, W(x), is important in several applications. Say I choose the branch on (0, infinity). Could I express this branch (or any other I choose) as an integral of well-defined functions?
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100