9709 P13 - Jun 2025 - Q11 - 10 marks
9710
\[f(x)=x^2+4ax+a\quad(x\in\mathbb R),\qquad g^{-1}(x)=\sqrt[3]{2x-4}\quad(x\in\mathbb R).\]
(a) The range of \(f\) is \([-33,\infty)\). Find all possible \(a\). [4]
(b) Instead \(fgg(0)=96\). Find \(a\). [6]
