# Understand the problem

Find all functions such that

holds for all .

holds for all .

##### Source of the problem

Benelux MO 2013

##### Topic

Functional Equations

##### Difficulty Level

Easy

##### Suggested Book

Functional Equations by BJ Venkatachala

# Start with hints

Do you really need a hint? Try it first!

Note that the RHS does not contain . Thus it should be possible to play with different values of to get rid of the inconvenient .

Taking , we get . Now show that . Thus $f(f(f(x)))=f(x)$.

Taking , we get . Now try to show that .

Taking we get the desired inequality from hint 3. Thus for all .

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