1992 IMO Problems/Problem 2
Problem
Let denote the set of all real numbers. Find all functions
such that
Solution
We notice that the right hand side of the equation has , therefore the only way that
produces that
is if
.
This makes the equation as
Since , then
, thus
and the equation holds true.
Only solution to this problem is
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See Also
1992 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |