" 22.Let "f:R rarr R" satisfying "|f(x)|<=x^(2)AA x in R" differentiable at "x=0." Then find "f(0)

" Let "f:R rarr R" satisfy relation "f(x)f(y)-f(xy)=x+y AA x,y in R" and "f(1)>0" .If "h(x)=f(x)f^(-1)(x)" ,then length of longest interval in which "h(sin x+cos x)" is strictly decreasing is."

Let f:R rarr R satisfying |f(x)|<=x^(2),AA x in R be differentiable at x=0. Then find f'(0)

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

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)

Let f : R rarr R satisfying l f (x) l <= x^2 for x in R, then (A) f' is continuous but non-differentiable at x = 0 (B) f' is discontinuous at x = 0 (C) f' is differentiable at x = 0 (D) None of these

The number of functions f:R rarr R satisfying f(x+y)=f(x)f(y)f(xy) where x,y in R and R is the set of real numbers is

If f:R rarr R satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all x,y in R , then (-f(10))/7 is ……… .

If f:R rarr R satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all x,y in R , then (-f(10))/7 is ……… .