1992 IMO Problems/Problem 2
Problem
Let denote the set of all real numbers. Find all functions such that
Solution
[quote=probability1.01]Set x = 0 to get . We'll let , so . Then
Since this holds for all , it follows that . Now we have . Note that f must be surjective since we may let y vary among all reals, and f must be injective since if , then . Finally, if , then there is some s.t. , and so . Hence f is strictly increasing. It is now clear that since , we must have for all x.[/quote]
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 |