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+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, then prove that f(x)>0AAx in Rdot

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)=sinalpha, the prove that f(x)>0AAx in Rdot

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

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

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+y)-f(x))/2=(f(y)-a)/2+x y for all real xa n dydot If f(x) is differentiable and f^(prime)(0) exists for all real permissible value of a and is equal to sqrt(5a-1-a^2)dot Then f(x) is positive for all real x f(x) is negative for all real x f(x)=0 has real roots Nothing can be said about the sign of f(x)

Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real xa n dydot If f(x) is differentiable and f^(prime)(0) exists for all real permissible value of a and is equal to sqrt(5a-1-a^2)dot Then (a) f(x) is positive for all real x (b) f(x) is negative for all real x (c) f(x)=0 has real roots (d)Nothing can be said about the sign of f(x)

Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real x and ydot If f(x) is differentiable and f^(prime)(0) exists for all real permissible value of a and is equal to sqrt(5a-1-a^2)dot Then a) f(x) is positive for all real x b) f(x) is negative for all real x c) f(x)=0 has real roots d) Nothing can be said about the sign of f(x)

Let f(x+y)=f(x)+f(y)+2xy-1 AAx,yinRR, If f(x) is differentiable and f'(0) = sin phi then -

If f(x+y)=f(x).f(y) for all real x,y and f(0)!=0, then the function g(x)=(f(x))/(1+{f(x)}^(2)) is: