Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The function $f$ is given by $f : x \mapsto 4 - 5x$ for $x \in \mathbb{R}$.
(a(i))[3]

Determine an expression for $f^{-1}(x)$ and locate the point where the graphs of $y = f(x)$ and $y = f^{-1}(x)$ intersect.

(a(ii))[3]

On one diagram, sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, and make the relationship between the two graphs clear.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct gradient-function expression at the intersection, giving $y=\frac{4-x}{5}$.

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