Given-f-xy-f-x-f-y-x-y-R-and-f-0-0-then-f-x-

Question Number 56921 by rahul 19 last updated on 26/Mar/19

G i v e n :

f (x y) = f (x) . f (y) \forall x, y ϵ R a n d f (0) \neq 0

t h e n f (x) = ?

Answered by mr W last updated on 26/Mar/19

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

w i t h y = 0

f (0) = f (x) f (0)

s i n c e f (0) \neq 0 \Rightarrow f (x) = 1

Commented by rahul 19 last updated on 26/Mar/19

S i r, h o w t o f i n d v a l u e o f n i f w e a s s u m e d

f (x) = x^{n} ?

Commented by mr W last updated on 27/Mar/19

f (x) \neq x^{n}, s i n c e f (0) \neq 0 .

f (x) = 1 i s t h e o n l y o n e s o l u t i o n .

Commented by rahul 19 last updated on 27/Mar/19

thank you sir!