f-R-R-g-R-R-f-xg-f-x-g-y-g-xy-f-x-g-y-d-fg-dx-

Question Number 821 by 123456 last updated on 17/Mar/15

f : R \to R

g : R \to R

f (x g) = f (x) g (y)

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

\frac{d (f g)}{d x} = ?

Answered by prakash jain last updated on 18/Mar/15

g (1) = f (1) + g (1) \Rightarrow f (1) = 0

f (x y) = f (x) g (y) \Rightarrow f (y) = f (1) g (y) = 0

f (x) = 0

g (x y) = g (y)

g (x) = g (1) \Rightarrow g (x) = C onstant

f (x) g (x) = 0