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

If 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?

If f(x) is continuous function , then

Statemant I : If f is continuous , then |f| is continuous Statement II : If |f| is continuous, then f is also continuous Which one of the following is true

Statement-1: If |f(x)| le |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.

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 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 continuous and real valued function on an interval, then - (i) f+g is continuous on the interval, (ii) fg is continuous on the interval, (iii) (f)/(g) is continuous on the interval. which of the statements given above are correct ?