Solution
= Solution
{c}
For $0\le x\le7$, we have $2\le2+x\le9$. Taking the nonnegative <square root> gives
$$
\boxed{G([0,7])=[\sqrt2,3]\subseteq[0,7].}
$$
The <derivative> is
$$
G'(x)=\frac1{2\sqrt{2+x}},
$$
so
$$
\boxed{|G'(x)|\le\frac1{2\sqrt2}<1\qquad(0\le x\le7).}
$$
In particular, the <mean value theorem> makes $G$ a <contraction mapping> on this interval.