A function $\displaystyle f$ is said to besymmetrically continuousat $\displaystyle x_0$ if

$\displaystyle \lim_{h{\rightarrow{0^+}}} [f (x_0 + h) - f (x_0 - h)] = 0.$

Show that if $\displaystyle f$ is continuous at $\displaystyle x_0$, it is symmetrically continuous there but not the conversely.