Find \({f^{ - 1}}(x)\) . 

Find \((f \circ g)(1)\) . 

interchanging x and y (seen anywhere)     (M1)

e.g. \(x = 2y - 1\)

correct manipulation     (A1)

e.g. \(x + 1 = 2y\)

\({f^{ - 1}}(x) = \frac{{x + 1}}{2}\)      A1     N2

[3 marks]

METHOD 1

attempt to find or \(g(1)\) or \(f(1)\)     (M1)

\(g(1) = 5\)     (A1)

\(f(5) = 9\)     A1     N2 

[3 marks]

METHOD 2

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

e.g. \(2(3{x^2} + 2) - 1\) , \(3{(2x - 1)^2} + 2\)

\((f \circ g)(1) = 2(3 \times {1^2} + 2) - 1\) \(( = 6 \times {1^2} + 3)\)     (A1)

\((f \circ g)(1) = 9\)     A1     N2

[3 marks]

This question was answered correctly by nearly all candidates.

This question was answered correctly by nearly all candidates. In part (b), there were a few who seemed unfamiliar with the notation for composition of functions, and attempted to multiply the functions rather than finding the composite, and there were a few who found the correct composite function but failed to substitute in \(x = 1\) to find the value.