Inverse function
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.