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.