Which of the following statements is/are correct ?There exist a function `f : [0,1] -> R` which is discontinuous at every pointcontinuous at every point in `[0,1]and |f(x)|` is continuous at every point in `[0,1]`

Which of the following statements is/are correct ?There exist a function f:[0,1]rarr R which is discontinuous at every pointcontinuous at every point in [0,1] and |f(x)| is continuous at every point in [0,1]

Prove that f(x){x-1,quad if x 2 is continuous at every point.

Consider the following statement in respect of a function f(x): 1. f(x) is continuous at x =a iff lim_(xtoa) f(x) exists. 2. If f(x) is continuous at a point, then (1)/(f(x)) is also continuous at that point. Which of the above, statements is/are corrent?

Consider the following statements in respect of a function f(x) I. f(x) continuous at x = a. if underset(xrarra)limf(x) exists II. If f(x) is continuous at a point, then (1)/(f(x)) is also continuous at the point. Which of the above statements is/are correct?

Consider the following statements: 1. The function f(x)=[x] where [.] is the greatest integer function defined on R, is continuous at all points except at x=0. 2. The function f(x)=sin|x| is continuous for all x""inR . Which of the above statements is/are correct?

The number of points at which the function f(x) = 1/(log|x|) is discontinuous are

Let f(x)={{:((e^(x)-1)/(x)",",xgt0),(0",",x=0):} be a real valued function. Which of the following statements is/are correct? 1. f(x) is right continuous at x=0. 2. f(x) is discontinuous at x=1. Seletct the correct answer using the code given below.

Let the set of all function f: [0,1]toR, which are continuous on [0,1] and differentiable on (0,1). Then for every f in S, there exists a c in (0,1) depending on f, such that :