\(g(x)=ax+b\implies g(g(x))=g(ax+b)=a(ax+b)+b=a^2x+ab+b\)
You have \(a^2=9\implies a=\pm3\), and \(ab+b=28\). If \(a=3\), then \(3b+b=4b=28\implies b=7\). If \(a=-3\), then \(-3b+b=-2b=28\implies b=-14\).
So the possible pairs are \((3,7)\) and \((-3,-14)\).
