1999 IMO Problems/Problem 6
Problem
Determine all functions such that
for all real numbers .
Solution
Let . Substituting , we get:
Now if c = 0, then:
which is not possible.
.
Now substituting , we get
.
Solving for , we get
This means because .
Specifically,
Using equations and , we get:
which gives
.
So, using this in equation , we get
as the only solution to this functional equation.
See Also
1999 IMO (Problems) • Resources | ||
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