If f is continuous on its domain D; then `|f|` is also continuous on D

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?

If f(x) is continuous function , then

Statement-1: If |f(x)|<=|x| for all x in R then |f(x)| is continuous at 0. Statement-2: If f(x) is continuous then |f(x)| is also continuous.

If f(x) is continuous then find a and b

If f and g are two continuous functions on their common domain D then f+g and f-g is continuous on D.

If f and g are two continuous functions on their common domain D then f.g and (f)/(g) is continuous on D provided g(x) is defined at that point.

Prove that cot x is continuous in its domain

f(x)=x+|x| is continuous for