A function `f: RvecR` satisfies the equation `f(x)f(y)-f(x y)=x+yAAx ,y in Ra n df(1)>0` , then `f(x)f^(-1)(x)=x^2-4` b. `f(x)f^(-1)(x)=x^2-6` c. `f(x)f^(-1)(x)=x^2-1` d.`` none of these

" A function "f:R rarr R" satisfies the equation "f(x)f(y)-f(xy)=x+y" and "f(y)>0" ,then "f(x)f^(-1)(x)=

If the function f(x) satisfies the relation f(x+y)=y(|x-1|)/((x-1))f(x)+f(y) with f(1)=2. then lim_(x rarr1)f'(x) is

Let f(x) be a function which satisfies the relation f(x+1)+f(2x+2)+f(1-x)+f(2+x)=x+1 AA x in R then value of [f(0)] is

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+y)/(2))=(f(x)+f(y))/(2),x,y in R, if f'(0)=-1, then f'((x)/(2))=

A real valued function f(x) satisfies the functional equation f(x-y)=f(x)f(y)-f(a-x)f(a+y) where a is a given constant and f(0), f (2a-x)=

A function f:R rarr[1,oo) satisfies the equation f(xy)=f(x)f(y)-f(x)-f(y)+2. If differentiable on R-{0} and f(2)=5,f'(x)=(f(x)-1)/(x). lambda then lambda2'f(1) b.3f'(1) c.(1)/(2)f'(1) d.f'(1)

Suppose the function f satisfies the conditions f(x+y)=f(x)f(y)AA x,y and f(x)=1+xg(x) where Lt_(x)rarr0(x)=1. show that f'(x) exists and f(x)=f(x)AA x

A function y=f(x) satisfies (x+1)f'(x)-2(x^(2)+x)f(x)=((e^(x))^(2))/((x+1)),AA x>1 If f(0)=5, then f(x) is