If f(x) is polynomial function such that `f(x) +f'(x) +f"(x)+f"'(x)=x^3` and `g(x)=int(f(x))/x^3` and `g(1)=1` then g(e) is

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

g(x) is inverse function of f(x). find f'(x) or f'(1) if g(x)=x^(^^)3+e^(^^)(x/2)

If f(x)=|x-1| and g(x)=f(f(f(x))) then for x>2,g'(x)=

Let f(x) be a function such that f(x)*f(y)=f(x+y),f(0)=1,f(1)=4. If 2g(x)=f(x)*(1-g(x))

If f(x) and g(x) are polynomial functions of x, then domain of (f(x))/(g(x)) is

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

If f(x)=(ax^(2)+b)^(3), then find the function g such that f(g(x))=g(f(x))

If f(x)=|x-1|" and "g(x)=f(f(f(x))) , then for xgt2,g'(x) is equal to

Let f and g be differentiable functions such that: xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R Also, f(x)gt0 and g(x)gt0 AA x in R int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R and g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R Now answer the question: f(g(0))+g(f(0))= (A) 1 (B) 2 (C) 3 (D) 4