Answer is : B. continuous but not differentiable at x = 2
For continuity left hand limit must be equal to right hand limit and value at the point.
Continuity at x = 2.
For continuity at x = 2,
f(2) = 1+2 = 3
∴ f(x) is continuous at x = 2
Now for differentiability.
= \(\lim\limits_{h\rightarrow0}\frac{h}{-h}\)
= -1
As, f’(2-) is not equal to f(2+)
∴ f(x) is not differentiable.