A function is defined by

$f(x)=a|x+p|+qx\inℝ$

where $a,p,q\inℝ$.

The graph of $y=f(x)$is shown below, where

• $A(3,5)$ is the local maximum point

• $(0,-7)$ is the $y$-intercept

Find the values of $a,p$ and $q.$

Show that $ff(x)=\frac{ax+b}{x-3}$ where $a$ and $b$ are integers to be found.

Find the exact value of the constant $a$ for which

$f({a}^{2}+2)=g(a)$

This question has 3 part(s).