A-LevelMathematicsFunctions9709/12 · Oct/Nov 2017 · Q26 Marks

A function f is defined by f : x → 4 – 5x for x ∈ R.

(i)Find an expression for f⁻¹(x) and find the point of intersection of the graphs of y = f(x) and y = f⁻¹(x).[3]
(ii)Sketch, on the same diagram, the graphs of y = f(x) and y = f⁻¹(x), making clear the relationship between the graphs.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

f⁻¹(x) = (4-x)/5 (B1) OE
Equate a valid attempt at f⁻¹ with f, or with x, or f with x (M1)
(2/3, 2/3) or (0.667, 0.667) (A1) Both coordinates.
Line y = 4 – 5x – must be straight, through approximately (0,4) and intersecting the positive x axis near (1,0) as shown. (B1)
Line y = (4-x)/5 – must be straight and through approximately (0, 0.8). No need to see intersection with x axis. (B1)
A line through (0,0) and the point of intersection of a pair of straight lines with negative gradients. This line must be at 45° unless scales are different in which case the line must be labelled y=x. (B1)

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