The functions $f$ and $g$ are given for every real value of $x$ by $f(x) = (3x - 2)^2 + k$ and $g(x) = 5x - 1$, with $k$ a constant.
(a)[4]
Since the range of $fg$ is $fg(x) \geq 39$, determine the value of $k$.
(b)[2]
For this value of $k$, determine the range of $fg$.
(c)[3]
The function $h$ is defined for every real value of $x$ and satisfies $gh(x) = 35x + 19$. Find an expression for $g^{-1}(x)$ and hence, or otherwise, find an expression for $h(x)$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set up an expression for $gf(x)$” …