Let `f(x+y)=f(x)f(y)` for all `x,y in R`and `f(0)!=0`. Let `phi(x)=f(x)/(1+f(x)^2)`. Then prove that `phi(x)-phi(-x)=0`

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0 . Then f(x) must be

Let f(x+2y)=f(x)(f(y))^(2) for all x,y and f(0)=1. If f is derivable at x=0 then f'(x)=

Let phi(a)=f(x)+f(2ax) and f'(x)>0 for all x in[0,a]. Then ,phi(x)

Let f(x+y)=f(x).f(y) for all x, y in R and f(x)=1+x phi(x)log3. If lim_(xrarr0)phi(x)=1, then f'(x) is equal to

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

Let f(x+y)=f(x)f(y) for all x,y in R suppose that f(3)=3,f(0)!=0 and f'(0)=11, then f'(3) is equal

If f(x+y)=f(x)*f(y) for all real x,y and f(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^(2)) is an even function.

Let f(x+y)=f(x)*f(y) for all x y where f(0)!=0 .If f(5)=2 and f'(0)=3 then f'(5) is equal to