# Understand the problem

Find all real numbers for which there exists a non-constant function satisfying the following two equations for all

i) and

ii)

i) and

ii)

##### Source of the problem

Baltic Way 2016

##### 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!

Show that the choices work.

Show that . As we have already dealt with , this gives .

Hint 3 gives . As has already been dealt with, we must consider the option .

Hint 3 gives . As , we have . This contradicts the fact that is non-constant. Hence, are the only options.

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