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.