Let `f(x+y)=f(x)+f(y)+2x y-1` for all real `xa n dy` and `f(x)` be a differentiable function. If `f^(prime)(0)=cosalpha,` the prove that `f(x)>0AAx in Rdot`

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

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

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is

If f(x)= y = (ax-b)/(cx-a) , then prove that f(y) = x

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx)

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.

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists for all x, f(2) = 4. Then, f(5) is

f(x+ y) = f(x) f(y) , For AA x and y . If f(3)= 3 and f'(0) =11 then f'(3)= …….