Continuity of a function

given the piecewise function

8-3x if x<4
10 if x=4
4/x-5 if x>4

a) find f(4)- Do I just plug in to where I see x=4?
b) compute limx-->4+ and limx-->4-
c) is f(x) continuous

a) f(4) = 10, by definition of f.

b) lim(x→4+) f(x)
= lim(x→4+) 4/(x-5), since x > 4
= -4.

lim(x→4-) f(x)
= lim(x→4-) (8 - 3x), since x < 4
= -4.

c) By part b, lim(x→4) f(x) = -4.

However, since lim(x→4) f(x) ≠ f(4), f is not continuous at x = 4.