How to solve this one?

Question

Check whether lim(x→−2) f(x) exists or not, where 

f(x)= {3x+2 , x<−2; x²+3x−1, x≥−2}

Answer 1

f(-2)=-3

Near but less than -2,f(x) is near -4.

f(x) is discontinuous at x=-2, i.e. no limit exists.

Answer 2

The limit of f(x) as approaches -2 from the left is 3(-2) + 2 = -4

The limit of f(x) as x approaches -2 from the right is (-2)² + 3(-2) - 1 = -3

Since the one-sided limits are unequal, lim_x→-2 f(x) does not exist.