Let be a function such that for all and and for all where is continuous and

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

f(x)

be a function such that

f(x + y) = f(x) + f(y)

for all

x

and

y

and

f(x) = (2x^2 + 3x) \cdot g(x)

for all

x

where

g(x)

is continuous and

g(0) = 3

. Then,

f'(x)

is equal to (1) 6 (2) 9 (3) 8 (4) None of these