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,

L.H.L =

R.H.L =

f(2) = 1+2 = 3

∴ f(x) is continuous at x = 2

Now for differentiability.

=-1

As, f’(2^-) is not equal to f(2⁺)

∴ f(x) is not differentiable.