(i)[5]
In the case where $f(-2) = 4a^2 - b + 8$ and $f(-3) = 7a^2 - b + 14$, determine the possible values of $a$ and $b$.
(ii)[5]
When $a = 1$ and $b = -1$, determine an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The function $f$ is defined by $f(x) = a^2x^2 - ax + 3b$ for $x \leq \frac{1}{2a}$, with $a$ and $b$ as constants.