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Date November 2016 Marks available 2 Reference code 16N.2.sl.TZ0.1
Level SL only Paper 2 Time zone TZ0
Command term Find Question number 1 Adapted from N/A

Question

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

Find \(f(8)\).

[2]
a.

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

[2]
b.

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

[3]
c.

Markscheme

attempt to substitute \(x = 8\)     (M1)

eg\(\,\,\,\,\,\)\({8^2} + 2 \times 8 + 1\)

\(f(8) = 81\)    A1     N2

[2 marks]

a.

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]

b.

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]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2 - Functions and equations » 2.1 » Domain, range; image (value).
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