Find $f(8)$.

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

Solve $(g \circ f)(x) = 0$.

attempt to substitute $x = 8$     (M1)

eg$\,\,\,\,\,$${8^2} + 2 \times 8 + 1$

$f(8) = 81$    A1     N2

[2 marks]

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

eg$\,\,\,\,\,$$f(x - 5),{\text{ }}g\left( {f(x)} \right),{\text{ }}\left( {{x^2} + 2x + 1} \right) - 5$

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

[2 marks]

valid approach     (M1)

eg     $x = \frac{{ - 2 \pm \sqrt {20} }}{2}$, 

$1.23606,{\text{ }} - 3.23606$

$x = 1.24,{\text{ }}x =  - 3.24$     A1A1     N3

[3 marks]