If `f(x-y), f(x) f(y) and f(x+y) ` are in A.P. for all `x, y in R` and f(0)=0. Then,

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

Let f be a real function such that f(x-y), f(x)f(y) and f(x+y) are in A.P. for all x,y, inR. If f(0)ne0, then

Le f : R to R and g : R to R be functions satisfying f(x+y) = f(x) +f(y) +f(x)f(y) and f(x) = xg (x) for all x , y in R . If lim_(x to 0) g(x) = 1 , then which of the following statements is/are TRUE ?

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 : R to R be a function given by f(x+y)=f(x)f(y) for all x , y in R If f(x) ne 0 for all x in R and f'(0) exists, then f'(x) equals

abs(f(x)-f(y))le(x-y)^2 forall x,y in R and f(0)=1 then

Let f:R in R be a function given by f(x+y)=f(x) f(y)"for all"x,y in R "If "(x) ne 0,"for all "x in R and f'(0)=log 2,"then "f(x)=

Let f(x) be a differentiable function satisfying the condition f((x)/(y)) = (f(x))/(f(y)) , where y != 0, f(y) != 0 for all x,y y in R and f'(1) = 2 The value of underset(-1)overset(1)(int) f(x) dx is