Let be a function satisfying and

MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions

Problem

Let

f: R \to R

be a function satisfying

f\left(\frac{xy}{2}\right) = \frac{f(x)f(y)}{2}, \forall x, y \in R

and

f(1) = f'(1) \neq 0

. Then,

f(x) + f(-x)

is (for all non-zero real values of

x

) (1) constant (2) can't be discussed (3)

\frac{1}{x}

(4)

\frac{1}{x^2}