Shown below are the graphs of \(y = f(x)\) and \(y = g(x)\).

If \((f \circ g)(x) = 3\), find all possible values of x.

\(g(x) = 0{\text{ or 3}}\)     (M1)(A1)

x = –1 or 4 or 1 or 2     A1A1

Notes: Award A1A1 for all four correct values,

A1A0 for two or three correct values,

A0A0 for less than two correct values.

Award M1 and corresponding A marks for correct attempt to find expressions for f and g.

[4 marks]

A small number of candidates gave correct and well explained answers. Many candidates answered the question without showing any kind of work and in many cases it was clear that candidates were guessing and clearly did not know about composition of functions. A number of candidates attempted to find expressions for both functions but made little progress and wasted time.