(i)[3]
State the range of $f$ in terms of $c$ and determine the least possible value of $c$.
(ii)[6]
The function $g$ is given by $g : x \mapsto ax + b$ for $x \geq 0$, where $a$ and $b$ are positive constants. It is stated that, when $c = 0$, $gf(1) = 11$ and $fg(1) = 21$. Write two equations in $a$ and $b$, then solve them to determine $a$ and $b$.