Question

Let \(X, Y, Z\) be metric spaces. \(f: X \rightarrow Y\) is called uniformly continuous if
\(\forall \epsilon > 0 \quad \exists \delta > 0 \quad \forall x, y \in X : d_{x}(x,y) \leq \delta \Rightarrow d_{Y}(f(x),f(y))\leq \epsilon \)
Show:
a) \(f:X \rightarrow Y\) \(and\) \(g:Y\rightarrow Z \)are uniformly continuous \(\Rightarrow g o f : X \rightarrow Z\) is uniformly continuous