f(xy)=f(x)f(y)" is true for all "

If f(x+y)=f(x)+f(y) -xy -1 for all x, y in R and f(1)=1 then f(n)=n, n in N is true if

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

A function f:RtoR is such that f(x+y)=f(x).f(y) for all x.y inR and f(x)ne0 for all x inR . If f'(0)=2 then f'(x) is equal to

if f(xy) = f(x) f(y) for all x and y and if f(x) is continuous at x = 1, then show that it is continuous for all x except 0

Let f'(x) exists for all x!=0 and f(xy)=f(x)+f(y) for all real x,y. Prove that f(x)=k log x where k is aconstant.

Let f(x+y)=f(x)+f(y)+2xy-1 for all real x and f(x) be a differentiable function.If f'(0)=cosalpha, the prove that f(x)>0AA x in R

Let f(x) be a differentiable function which satisfies the equation f(xy)=f(x)+f(y) for all x>0,y>0 then f'(x) equals to

The f(x) is such that f(x+y) = f(x) + f(y) , for all reals x and y xx then f(0) =

Let f(xy)=f(xy) f(y)"for all"x gt 0, y gt 0 and f(1+x)=1+x[1+g(x)],"where "lim_(x to 0) , where g(x),"then " int(f(x))/(f'(x)) dx is