(a(i))[3]
Find the values for $a$ and $b$.
(a(ii))[2]
Find the greatest possible value for $q$.
(a(iii))[1]
Find the range for $fg$.
(a(iv))[3]
Find an expression for $(fg)^{-1}(x)$ and state the domain for $(fg)^{-1}$.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The function $f$ is defined by $f(x) = 2x + 3$ when $x \geq 0$. The function $g$ is defined by $g(x) = ax^2 + b$ for $x \leq q$, where $a$, $b$ and $q$ are constants. The composite function $fg$ satisfies $fg(x) = 6x^2 - 21$ for $x \leq q$.