The function $f$ is given by $f(x) = x^2 - 4x + 7$ when $x > 2$.
(i)[3]
Express $f(x)$ in the form $(x-a)^2 + b$ and so determine the range of $f$.
(ii)[3]
Obtain an expression for $f^{-1}(x)$ and give the domain of $f^{-1}$.
(iii)[1]
The function $g$ is given by $g(x) = x - 2$ for $x > 2$. The function $h$ satisfies $f = hg$ and has domain $x > 0$. Obtain an expression for $h(x)$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Writes the quadratic as $(x-2)^2$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI