`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`

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

There exists a function f(x) satisfying 'f (0)=1,f(0)=-1,f(x) lt 0,AAx and

If f:R rarr R is continous function satisying 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

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

If f:R to R is a continuous function satisfying f(0)=1 and f(2x)-f(x)=x"for all x"in R and lim_(x to oo) {f(x)-f((x)/(2^(n)))}=P(x), P(x), is

Let f:R-{0}rarr R be a function satisfying f((x)/(y))=(f(x))/(f(y)) for all x,y,f(y)!=0 .If f'(1)=2024 ,then