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
Climate change increases risk of crop slowdown in next 20 years
Researcher part of team studying ways to better predict intensity of hurricanes
New molecule puts scientists a step closer to understanding hydrogen storage