[f=R rarr R" beatunction such that "f((z+g)/(3))=(f(x)+f(s))/(3),f(0)=0],[f(0)=3" .then "]

Let f:R rarr R be a function such that f((x+y)/(3))=(f(x)+f(y))/(3),f(0)=0 and f'(0)=3

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R rarr R-{3} be a function such that for some p>0,f(x+p)=(f(x)-5)/(f(x)-3) for all x in R. Then,period of f is

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

If f:R rarr[0,oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), then prove that f(x) is periodic and find its period.

Let f:R rarr R satisfying f((x+y)/(k))=(f(x)+f(y))/(k)(k!=0,2). Let f(x) be differentiable on R and f'(0)=a then determine f(x)

If f: R rarr [0, oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x) , and f(x) is periodic then its period is

Let f:R rarr R be a function satisfying condition f(x+y^(3))=f(x)+[f(y)]^(3) for all x,y in R If f'(0)>=0, find f(10)

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