`f:R^+ ->R` is a continuous function satisfying `f(x/y)=f(x)-f(y) AAx,y in R^+`.If f'(1)=1,then (a)f is unbounded (b)`lim_(x->0)f(1/x)=0` (c)`lim_(x->0)f(1+x)/x=1` (d)`lim_(x->0)x.f(x)=0`

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfy f((4x)/y)=f(x)-f(y) for all x,y and f(4e) = 1, then (a) f(x) = In 4x(b) f(x) is bounded (c) lim_(x->0) f(1/x)=0 (d) lim_(x->0)xf(x)=0

If f(x) is a continuous function satisfying f(x)f(1/x) =f(x)+f(1/x) and f(1) gt 0 then lim_(x to 1) f(x) is equal to

Let f(x) be defined for all x>0 and be continuous.Let f(x) satisfy f((4x)/(y))=f(x)-f(y) for all x,y and f(4e)=1, then (a) f(x)=ln4x( b) f(x) is bounded (c) lim_(x rarr0)f((1)/(x))=0 (d) lim_(x rarr0)xf(x)=0

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

If f:R rarr R is continuous function satisfying f(0) =1 and f(2x) -f(x) =x, AAx in R , then lim_(nrarroo) (f(x)-f((x)/(2^(n)))) is equal to

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

If f(x) is a function satisfying f(x)-f(y)=(y^y)/(x^x)f((x^x)/(y^y))AAx , y in R^*"and"f^(prime)(1)=1 , then find f(x)