Find all functions such that for all

Singapore Team Selection Test 2008

Functional Equations

Medium

Functional Equations by BJ Venkatachala

Do you really need a hint? Try it first!

Play with choices of belonging to . Show that .

Play with choices of from the set .

Following hint 2, you should be able to get equations that can be added to cancel some terms.

Putting

we get
Putting we get
gives

Adding, we get .

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