Please recall the definition of a function, either increasing or decreasing on an interval
(v.s. def monotonous function).
Example 5.7.2
Take

.
- This function is continuous and strictly increasing on
, thus it is a bijection of
onto
.
- By Prop. 5.1,
and
.
Therefore

and

is a bijection of

onto

. The graphs of the function

and of its inverse function are displayed in Figure
11. Note that the computation of an explicit formula for the function

is very hard. We can do it using a Computer Algebra System.
Figure 11:
Graphs of two inverse functions
 |
A consequence of this is that any equation of the form
has a unique solution in
.