Functions $f$ and $g$ are given by $f : x \mapsto 2x - 3$, $x \in \mathbb{R}$, and $g : x \mapsto x^2 + 4x$, $x \in \mathbb{R}$. The function $h$ is given by $h : x \mapsto x^2 + 4x$ for $x \geq k$, and it is stated that $h$ is invertible.
(i)[2]
Solve $f(x) = 11$.
(ii)[2]
Find the range for $g$.
(iii)[3]
Find the values of $x$ such that $g(x) > 12$.
(iv)[3]
Find the value of the constant $p$ for which $g(x)=p$ has two repeated roots.
(v)[1]
State the least possible value of $k$.
(vi)[4]
Find a formula for $h^{-1}(x)$.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sets up the equation $2(2x-3)=3$” …