The function $f$ has the rule $f(x) = 4x^2 - 12x + 13$ for $p < x < q$, where $p$ and $q$ are constants. The function $g$ has the rule $g(x) = 3x + 1$ for $x < 8$.
(a)[2]
Express $4x^2 - 12x + 13$ in the form $(2x + a)^2 + b$, where $a$ and $b$ are constants.
(b)[3]
Given that the composite function $gf$ can be formed, find the least possible value of $p$ and the greatest possible value of $q$.
(c)[1]
Find a formula for $gf(x)$.
(d)[3]
The function $h$ has rule $h(x) = 4x^2 - 12x + 13$ for $x < 0$. Find an expression for $h^{-1}(x)$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Completing the square gives $(2x-3)^2+4$.” …