If to change an argument and a function by roles, then x will be a function of y . In this case we say about a new function, called an inverse function . Assume, we have a function:
where u is an argument and v is a function. If to change them by roles, we’ll receive u as a function of v :
If to mark in both of the functions an argument as x and a function as y , then we have two functions:
each of which is an inverse one to another.
E x a m p l e s . These functions are inverse one to another:
1) sin x and Arcsin x , because if y = sin x , then x = Arcsin y ;
2) cos x and Arccos x , because if y = cos x , then x = Arccos y ;
3) tan x and Arctan x , because if y = tan x , then x = Arctan y ;
4) e x and ln x , because if y = e x , then x = ln y.