How to find the period of this function

[abhip]

f(x)+f(x+4)=f(x+2)+f(x+6) where all functions are real valued

 

[Char. Limit]

Write g(x)=f(x)+f(x+4). Then it's easy to see that the left-hand side is g(x) and the right hand side is g(x+2), so g(x)=g(x+2). That seems to be where I would start.

 

[abhip]

Thank you very much for the approach it was helpful but after setting g(x)=f(x)+f(x+4) and knowing the fact g(x) has a period 2 how to relate if to f(x).Is there any approach to do so or do i have to opt for trial and error.