It is given that

Case I: x = 0

We can see that f is defined at 0 and its value at 0 is 0.

= 0

Hence, f is continuous at x = 0.

Case II: x = 1

We can see that f is defined at 1 and its value at 1 is 1.

= 1

= 5

Hence, f is not continuous at x = 1.

Case III: x = 2

We can see that f is defined at 2 and its value at 2 is 5.

= 5

Hence, f is continuous at x = 2.