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

If a function f satisfies f (f(x))=x+1 for all real values of x and if f(0) = 1/2 then f(1) is equal to

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), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x) is a differentiable real valued function satisfying f''(x)-3f'(x) gt 3 AA x ge 0 and f'(0)=-1, then f(x)+x AA x gt 0 is

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The number of solution(s) of the equation |x^(2)+x-6|=f(x)+g(x) is/are

Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The total number of root(s) of the equation f(x)=g(x) is/ are

A function f:RtoR is such that f(x+y)=f(x).f(y) for all x.y inR and f(x)ne0 for all x inR . If f'(0)=2 then f'(x) is equal to