Let be a derivable function at and ( )

MATHEMATICS · Single correct · ISC · Mathematics · Calculus · Derivatives of standard functions via chain rule

Problem

Let f(x)f(x) be a derivable function at x=0x = 0 and f(x+yK)=f(x)+f(y)Kf\left(\frac{x+y}{K}\right) = \frac{f(x) + f(y)}{K} (K∈R,K≠0,2K \in \mathbb{R}, K \neq 0, 2). Then, f(x)f(x) is (1) even function (2) neither even nor odd function (3) either zero or odd function (4) either zero or even function

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