Find \({f^{ - 1}}(x)\) .

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

Find \((f \circ g)(3.5)\) .

interchanging x and y (may be seen at any time)     (M1)

evidence of correct manipulation     (A1)

e.g. \(x = 2y + 4\)

\({f^{ - 1}}(x) = \frac{{x - 4}}{2}\) (accept \(y = \frac{{x - 4}}{2},\frac{{x - 4}}{2}\) )     A1     N2

[3 marks]

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

e.g. \(f(7{x^2}){\text{, }}2(7{x^2}) + 4{\text{, }}7{(2x + 4)^2}\)

\((f \circ g)(x) = 14{x^2} + 4\)     A1     N2

correct substitution     (A1)

e.g. \(7 \times {3.5^2}\) , \(14{(3.5)^2} + 4\)

\((f \circ g)(3.5) = 175.5\) (accept 176)     A1     N2

[2 marks]

All parts of this question were well answered by most of the candidates. Some misunderstood part (a) and found the derivative or the reciprocal, indicating they were not familiar with the notation for an inverse function. Occasionally, the composition symbol was mistaken for multiplication. Additionally, some candidates composed in the incorrect order.

All parts of this question were well answered by most of the candidates. Some misunderstood part (a) and found the derivative or the reciprocal, indicating they were not familiar with the notation for an inverse function. Occasionally, the composition symbol was mistaken for multiplication. Additionally, some candidates composed in the incorrect order.

All parts of this question were well answered by most of the candidates. Some misunderstood part (a) and found the derivative or the reciprocal, indicating they were not familiar with the notation for an inverse function. Occasionally, the composition symbol was mistaken for multiplication. Additionally, some candidates composed in the incorrect order.