16N.2.SL.TZ0.S_1

pestleMathematicsAISLPaper 216N· sl-2-2-functions-notation-domain-range-and-inverse-as-reflectionsource ↗

Let $f(x) = {x^2} + 2x + 1$ and $g(x) = x - 5$ , for $x \in \mathbb{R}$ .

Find $f(8)$ .

[2]

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

[2]

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

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

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 $x = \frac{{ - 2 \pm \sqrt {20} }}{2}$ , N16/5/MATME/SP2/ENG/TZ0/01.c/M

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

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

[3 marks]

Examiners’ report

[N/A]