If `0ltalt1` and f is defined as `f(x)={[x^(a),x>0],[0,x=0]}`,then which of the following is true.

If f:R in R is defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2 , the which of the following is true:

Let f:R rarr R be defined as f(x)={0,x is irrational sin|x|,x is rational Then which of the following is true?

Let f(x)=x sin(e^((1)/(x))) for x!=0 and for x=0 which of the following is true?

If f ''(x)|le 1 AA x in R, and f (0) =0=f' (0), then which of the following can not be true ?

Function f(x),g(x) are defined on [-1,3] and f'(x)>0,g'(x)>0 for all x in[-1,3], then which of the followingis always true?

If f(0)=f(1)=f(2)=0 and function f (x) is twice differentiable in (0, 2) and continuous in [0, 2]. Then, which of the following is(are) true ?