If `2f(x)=f(x y)+f(x/y)` for all positive values of `x and y,f(1)=0 and f'(1)=1,` then `f(e)` is.

If f(x)f(y) = f(x) + f(y) + f(xy) -2 for all real values of x and y and f(2) = 5, find f(4) and f(1/4) .

If f(x+y)=f(x)+f(y) for all real x and y, show that f(x)=xf(1) .

Let f((x+y)/(2))=1/2 |f(x) +f(y)| for all real x and y, if f '(0) exists and equal to (-1), and f(0)=1 then f(2) is equal to-

Let f((x+y)/2) = (f(x)+f(y))/2 for all real values of x and y. If f^(')(0) exists and equals -1 and f(0) =1, then f^(')(2) is equal to

If for all values of x and y , f(x+y) =f(x) f(y) and f(5) =2, f'(0)=3, then the value of f'(5) is-

If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then what is the value of f '(5)?

f(x+(1)/(y))+f(x-(1)/(y))=2f(x)*f((1)/(y)) for all xy in R-{0} and f(0)=(1)/(2), then f(4) is

If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2)) then:

If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2)) then:

Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y . If f'(0) exits and equals -1 and f(0) =1 , then find f(2) .