Consider function satisfies the relation

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Consider function

f(x)

satisfies the relation

f(x+y^3) = f(x) + f(y^3)

\forall x, y \in R

and differentiable for all

x

. (1) Statement I If

f'(2) = a

, then

f'(-2) = a

(2) Statement II

f(x)

is an odd function.