Question

Let f(0) not equal to 0 and for x and y belong to R, 2f(x)f(y)= f(x+y)+f(x-y) is always true, then, express f(2x) in terms of f(x).

Answer 1

What did you try?

Answer 2

confused.

Answer 3

How about this, could you express f(2t) in terms of f(t)?

Answer 4

If you could find the f(2t) in the equation, then you probably can do this problem.

Answer 5

put x=y

Answer 6

yeap.
I got it.

let x=y
so 2*f^2(x)=f(2x)+k because f(0)=k
so f(2x)=2f^2(x)-k

Answer 7

seems correct.