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Date	May 2018	Marks available	3	Reference code	18M.1.sl.TZ1.1
Level	SL only	Paper	1	Time zone	TZ1
Command term	Find	Question number	1	Adapted from	N/A

Question

Let $f\left( x \right) = \sqrt {x + 2}$ for x ≥ 2 and g(x) = 3x − 7 for $x \in \mathbb{R}$ .

Write down f (14).

[1]

Find $\left( {g \circ f} \right)$ (14).

[2]

Find g⁻¹(x).

[3]

Markscheme

f (14) = 4 A1 N1

[1 mark]

attempt to substitute (M1)

eg g (4), 3 × 4 − 7

5 A1 N2

[2 marks]

interchanging x and y (seen anywhere) (M1)

eg x = 3y − 7

evidence of correct manipulation (A1)

eg x + 7 = 3y

${g^{ - 1}}\left( x \right) = \frac{{x + 7}}{3}$ A1 N3

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2 - Functions and equations » 2.1 » Concept of function

$f:x \mapsto f\left( x \right)$ .

Show 29 related questions

18M.1.sl.TZ1.3c: On the grid above, sketch the graph of f −1.
18M.1.sl.TZ1.3b: Write down the range of f −1.
18M.1.sl.TZ1.3a.ii: Write down the value of f −1 (1).
18M.1.sl.TZ1.3a.i: Write down the value of f (0).
18M.1.sl.TZ1.1b: Find $\left( {g \circ f} \right)$ (14).
18M.1.sl.TZ1.1a: Write down f (14).
17M.2.sl.TZ2.3c: Write down the domain of $g$ .
17M.2.sl.TZ2.3b: On the grid above, sketch the graph of $g$ .
17M.2.sl.TZ2.3a: Write down the range of $f$ .
16M.1.sl.TZ1.1c: Find ${f^{ - 1}}(x)$ .
16M.1.sl.TZ1.1b: Find $(f \circ g)(x)$ .
16M.1.sl.TZ1.1a: Write down $g(2)$ .
08N.1.sl.TZ0.4b: Write down the range of ${f^{ - 1}}$ .
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13M.1.sl.TZ1.10a: Find the value of $f(0)$ .
13M.2.sl.TZ1.9c: Find the range of $f$ .
13M.2.sl.TZ1.9a: Write down $f(0)$ .
13M.1.sl.TZ2.4a.i: Write down the value of $f(2)$ .
13M.1.sl.TZ2.10c: find the $y$ -coordinate of P.
13M.1.sl.TZ2.10a: Write down the value of $g(3)$ , of $f'(3)$ , and of $h''(2)$ .
14M.1.sl.TZ2.3a(ii): Write down the value of ${f^{ - 1}}(1)$ .
14M.1.sl.TZ2.3a(i): Write down the value of $f( - 3)$ .
14M.1.sl.TZ2.3b: Find the domain of ${f^{ - 1}}$ .
17N.1.sl.TZ0.3c: On the grid, sketch the graph of ${f^{ - 1}}$ .
17N.1.sl.TZ0.3b.ii: Write down ${f^{ - 1}}(2)$ .
17N.1.sl.TZ0.3b.i: Write down $f(2)$ ;
17N.1.sl.TZ0.3a: Write down the range of $f$ .

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