Plz explain example 5

Dear Student,
Solution)

f (x) = |x| + 1, x < 0 = 0, x = 0 = |x| - 1, x > 0 Function definiton changes at x = 0 L . H . L . = \lim_{x \to 0^{-}} f (x) = \lim_{x \to 0^{-}} |x| + 1 = 0 + 1 L . H . L . = 1 R . H . L . = \lim_{x \to 0^{+}} f (x) = \lim_{x \to 0^{+}} |x| - 1 = 0 - 1 R . H . L . = - 1 As L . H . L . \neq R . H . L ., hence limit does not exist at x = 0 but it will exist at every other point . Hence a \in R - \{0\}

Regards!