Question -
Answer -
The given function f is 
At x =0,
It isevident that f is defined at 0 and its value at 0 is 0.
Therefore, f iscontinuous at x = 0
At x =1,
f is defined at 1 andits value at 1 is 1.
Theleft hand limit of f at x = 1 is,
Theright hand limit of f at x = 1 is,
Therefore, f isnot continuous at x = 1
At x =2,
f is defined at 2 andits value at 2 is 5.
Therefore, f iscontinuous at x = 2