f(x) + f(x+T) = 2 ; where T is a fixed positive number.
The solution is given as:
put x = x+T
then given equation becomes
f(x+T) + f(x+2T) = 2
subtract given equation from above. You'll get: f(x) = f(x+2T).
Hence 2T is the period of f(x).
I don't get it. wouldn't putting x = x+T change the value of the function? How come we are still equating it to 2? If the function value doesn't change then we are implicitly assuming that T is the period right?