If f(x) is a real-valued function discontinuous at all integral points lying in [0,n] and if `(f(x))^(2)=1, forall x in [0,n],` then number of functions f(x) are

Let 'f' be a real valued function defined for all x in R such that for some fixed a gt 0, f(x+a)= 1/2 + sqrt(f(x)-(f(x))^(2)) for all 'x' then the period of f(x) is

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

If f is a real-valued differentiable function such that f(x)f'(x)lt0 for all real x, then -

If f is a real-valued differentiable function such that f(x) f'(x)lt0 for all real x, then

The function f(x) is discontinuous only at x = 0 such that f^(2)(x)=1 AA x in R . The total number of such functions is

The function f(x) is discontinuous only at x = 0 such that f^(2)(x)=1 AA x in R . The total number of such functions is

The function f(x) is discontinuous only at x = 0 such that f^(2)(x)=1 AA x in R . The total number of such functions is

The function f(x) is discontinuous only at x = 0 such that f^(2)(x)=1 AA x in R . The total number of such functions is

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then