Question

if f(x) =|x|+|x+2| ,then
a) f(x) is continuous at x=0but not at x=2
b) f(x) is continuous at x=0 and at x= 2
c) f(x) is continuous at x=2 but not at x=0
d) none of these ​

Answer 1

Answer:

The correct answer is (b) .

Step-by-step explanation:

Concept :

(1).  If f(x) is a continuous function, then |f(x)| is also continuous function

(2). Sum of two continuous function is also a continuous function

Therefore since x is a continuous function |x| is also continuous function, and x+2 is a continuous function so |x+2| is also a continuous function and hence |x|+|x+2| is also a continuous function. Thus the correct option is (b).

Note : f(x) is continuous for all x so it is continuous at x= 0 and x=2 also