Let g: [a,b] --> [c,d] be a continuous function in $\displaystyle x_0\in $[a,b], and f: [c,d] --> R a continuous function in g($\displaystyle x_0$) $\displaystyle \in$ [c,d]

Show that f o g: [a,b] --> R defined by (f o g)(x) = f(g(x)) $\displaystyle \forall$x $\displaystyle \in$ [a,b] is continuous in $\displaystyle x_0 \in$ [a,b]