(a)[4]
If the range of $f$ is $f(x) \ge -33$, determine the possible values of $a$.
(b)[6]
If instead $fgg(0) = 96$, determine the value of $a$.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The function $f$ is given by $f(x) = x^2 + 4ax + a$ for every $x \in \mathbb{R}$, with $a$ a constant. The function $g$ is defined so that $g^{-1}(x) = \sqrt[3]{2x - 4}$ for every $x \in \mathbb{R}$.