ACJC P2 Q3

The function g is defined by

$g: x \mapsto \begin{cases} 2x, & \text{for }0 \le x \le \frac{1}{2} \\ 2-2x, & \text{for } \frac{1}{2} \le x \le 1 \end{cases}$

(ii) Explain why the composite function $gg$ exist.

(iii) Sketch the graph of $gg(x)$.