# 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:

*v*=

*u*

^{2},

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.*

### Related post:

- Graphical solving of inequalities
- Graphical solving of equations
- Elementary functions and their graphs
- Composite function
- Basic notions and properties of functions
- Coordinates. Graphical representation of functions
- Designation of functions
- Representation of function by formula and table
- Functional dependence between two variables
- Constants and variables