Let `f(x)` be defined for all `x > 0` and be continuous. Let `f(x)` satisfies `f(x/y)=f(x)-f(y)` for all `x,y and f(e)=1.` Then

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+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to

Let a function f be defined by f(x)=(x-|x|)/x for x ne 0 and f(0)=2. Then f is

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2 , then

If F :R to R satisfies f(x +y ) =f(x) + f(y) for all x ,y in R and f (1) =7 , then sum_(r=1)^(n) f(R ) is

Let sum_(k=1)^(10)f(a+k)=16(2^(10)-1), where the function f satisfies f(x+y)=f(x)f(y) for all natural numbers x, y and f(1) = 2. Then, the natural number 'a' is

Let f:R->R be a continuous function such that |f(x)-f(y)|>=|x-y| for all x,y in R ,then f(x) will be

If for a function f : R to R f (x +y ) =F(x ) + f(y) for all x and y then f(0) is

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then