Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The function $f$ is given by $f(x) = 10 + 6x - x^2$ for all $x \in \mathbb{R}$.

(a)[3]

Use completing the square to determine the range of $f$.

(b)[6]

It is stated that the graph of $y = g^{-1} f(x)$ meets the graph of $y = g(x)$ at just one point $P$. Determine the coordinates of $P$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Express $f(x)=a-(x-3)^2$ or $a-(3-x)^2$” …