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.