Given that `f(x) > g(x)` for all real `x, and f(0)=g(0)`. Then `f(x) < g(x)` for all x belong to `(a) `(0,oo) (b) `(-oo,0)` (c) `(-oo,oo)` (d) `none of these

f'(x) = g(x) and g'(x) =-f(x) for all real x and f(5)=2=f'(5) then f^2 (10) + g^2 (10) is

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0), then the value of k is

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________

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

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

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(x) and g(x) be functions which take integers as arguments. Let f(x + y) =f(x)+ g(y) + 8 for all intege x and y. Let f(x) = x for all negative integers x and let g (8) = 17 . Find f(0).

Given that f(x) = xg (x)//|x| g(0) = g'(0)=0 and f(x) is continuous at x=0 then the value of f'(0)

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f(x) and g(x) be defined and differntiable for all x ge x_0 and f(x_0)=g(x_0) f(x) ge (x) for x gt x_0 then