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 f:R rarr R be a differentiable function satisfying 2f((x+y)/(2))-f(y)=f(x) AA x , y in R ,if f(0)=5 and f'(0)=-1 , then f(1)+f(2)+f(3) equals

If f is a differentiable function satisfying 2f(x)=f(xy)+f((x)/(y)),AA x,y in R^(+), f(1)=0 and f'(1)=(1)/(ln6), then f(7776) =

Let f :R to R be a differentiable function satisfying: f (xy) =(f(x))/(y)+f(y)/(x) AAx, y in R ^(+) also f (1)=0,f '(1) =1 find lim _(x to e) [(1)/(f (x))] (where [.] denotes greatest integer function).

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

Let f be a differentiable function satisfying f(x+2y)=2yf(x)+xf(y)-3xy+1 AA x , y in R such that f'(0)=1 ,then value of f(8) is equal

Let f be a real valued differentiable function satisfying f(x+y)=f(x)+f(y)-xy-1,AA x,y in R and f(1)=1. Equation ofthe normal to the graph of f(x) at the point where y=f(x) cuts the y-axis,is

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to