Find ${g^{ - 1}}(x)$ .

Find $(f \circ g)(4)$ .

for interchanging x and y (may be done later)     (M1)

e.g. $x = 2y - 3$

${g^{ - 1}}(x) = \frac{{x + 3}}{2}$ (accept $y = \frac{{x + 3}}{2},\frac{{x + 3}}{2}$ )     A1     N2

[2 marks]

METHOD 1

$g(4) = 5$     (A1)

evidence of composition of functions     (M1)

$f(5) = 25$     A1 N3

METHOD 2

$f \circ g(x) = {(2x - 3)^2}$     (M1)

$f \circ g(4) = {(2 \times 4 - 3)^2}$     (A1)

= 25     A1     N3

[3 marks]

Many candidates performed successfully in finding the inverse function, as well as the composite at a specified value of x.

Many candidates performed successfully in finding the inverse function, as well as the composite at a specified value of x. Some candidates made arithmetical errors especially if they expanded the binomial before substituting $x = 4$ .