Find \((f \circ g)(x)\).

Solve the equation \((f \circ g)(x) = 0\).

attempt to form composite (in any order)     (M1)

eg\(\;\;\;f({x^3}),{\text{ }}{(2x + 3)^3}\)

\((f \circ g)(x) = 2{x^3} + 3\)     A1     N2

[2 marks]

evidence of appropriate approach     (M1)

eg\(\;\;\;2{x^3} =  - 3\), sketch

correct working     (A1)

eg\(\;\;\;{x^3} = \frac{{ - 3}}{2}\), sketch

\( - 1.14471\)

\(x = \sqrt[3]{{\frac{{ - 3}}{2}}}\;\;\;{\text{(exact), }} - 1.14{\text{ }}[ - 1.15,{\text{ }} - 1.14]\)     A1     N3

[3 marks]

Total [5 marks]

Generally well done, though there were some careless errors with the substitution into \(f\) in part (ai) and rearranging the equation in part (b). Although candidates understood that they were supposed to solve the equation \(2{x^3} + 3 = 0\), many wrote \(2{x^3} = 3\) or \(x = \sqrt {\frac{3}{2}} \). The majority of the candidates chose an algebraic method instead of using their GDC.

Generally well done, though there were some careless errors with the substitution into \(f\) in part (ai) and rearranging the equation in part (b). Although candidates understood that they were supposed to solve the equation \(2{x^3} + 3 = 0\), many wrote \(2{x^3} = 3\) or \(x = \sqrt {\frac{3}{2}} \). The majority of the candidates chose an algebraic method instead of using their GDC.