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) =cot x is discontinuous on set

The function f(x) =cot x is discontinuous on set

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

The function f(x)= xcos(1/x^2) for x != 0, f(0) =1 then at x = 0, f(x) is

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 the function f(x)=x^(2)sin((1)/(x)), AA x ne 0 is continuous at x = 0. Then, the vaue of the function at x = 0 is

Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The total number of root(s) of the equation f(x)=g(x) is/ are

If f(x) is a continuous function such that its value AA x in R is a rational number and f(1)+f(2)=6 , then the value of f(3) is equal to

Let f(x)={8^(1/x),x<0a[x],a in R-{0},xgeq0, (where [.] denotes the greatest integer function). Then (a) f(x) is Continuous only at a finite number of points (b)Discontinuous at a finite number of points. (c)Discontinuous at an infinite number of points. (d)Discontinuous at x=0