NDA Math Limit, Continuity and Differentiability

f(x)={

x2−5,	x≤3
√x+13,	x>3

lim

x→3−

f(x)=32−5=4

lim

x→3+

f(x)=√3+13=4
f(x)=4,therefore function is continuous at x=3
x2−5 is is a continuous and differentiable function in its entire domain.
Hence, for 0
f(x) is continuous and differentiable.
So neither of the statements is correct