Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of `f(x).f(-x)` for all x is

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x ,AAx in Rdot Then find the value of f(0)dot

The function f:R→R satisfies f(x^2 ).f ′′ (x)=f ′ (x).f ′ (x^2 ) for all real x. Given that f(1)=1 and compute the value of f ′ (1)+f ′′ (1) .

Let f(x) is a polynomial satisfying f(x).f(y) = f(x) +f(y) + f(xy) - 2 for all x, y and f(2) = 1025, then the value of lim_(x->2) f'(x) is

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R and f(0)!=0 Then g(x)=f(x)/(1+[f(x)]^2) is

Let f : W-> W be a given function satisfying f(x) = f(x-1)+f(x-2) for x<=2 .If f(0)=0 and f(1)=1 , ther find the value of f(2) + f(3) + f(4) + f(5) + f(6) .

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,and f(0)=3, and if f(3)=3, then the value of f(-3) is ______________

Let f be a function such that f(x+y)=f(x)+f(y)" for all "x and y and f(x) =(2x^(2)+3x) g(x)" for all "x, " where "g(x) is continuous and g(0) = 3. Then find f'(x)

Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and f(x)=1+xg(x) where underset(x to 0)lim g(x)=1 . Then f'(x) is equal to