Question

Let f (x) = | x | + | x − 1|, then

विकल्प

•  f (x) is continuous at x = 0, as well as at x = 1

• f (x) is continuous at x = 0, but not at x = 1

• f (x) is continuous at x = 1, but not at x = 0

• none of these

Answer 1

f (x) is continuous at x = 0, as well as at x = 1 

Since modulus function is everywhere continuous , 

\[\left| x \right| \text{ and } \left| x - 1 \right|\]  are also everywhere continuous.

Also, 
It is known that if f and g are continuous functions, then f + g will also be continuous.

Thus, ​ ​

\[\left| x \right| + \left| x - 1 \right|\] is everywhere continuous.

Hence, 

\[f\left( x \right)\]  is continuous at 

\[x = 0 \text{ and } x = 1\]