Question

各位数学高手，请问这一题怎么解？

Answer 1

(a)x=-2,x=2,x=4
(b)x=-2 is continuous from the left；
x=2 is continuous from the right；
x=4 is continuous from the left；

Answer 2

(a) 问哪里不连续，显然是在 x = -4, -2, 2, 4 这四处不连续，理由是左极限和右极限不相等，即该点的极限不确定。When x = -4, -2, 2, or 4, f is discontinuous since the limit by the left does not equal to the one by the right.
(b) 问上问中不连续的点是否单侧连续，显然 x = -4 左右都不连续，x = -2 左连续，x = 2, 4 右连续。When x = -4, f is neither continuous. When x = -2, f is continuous from the left. When x = 2 or 4, f is continuous from the right.