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Date	May 2017	Marks available	2	Reference code	17M.1.hl.TZ2.2
Level	HL only	Paper	1	Time zone	TZ2
Command term	Write down	Question number	2	Adapted from	N/A

Question

The function $f$ is defined by $f(x) = 2{x^3} + 5,{\text{ }} - 2 \leqslant x \leqslant 2$ .

Write down the range of $f$ .

[2]

Find an expression for ${f^{ - 1}}(x)$ .

[2]

Write down the domain and range of ${f^{ - 1}}$ .

[2]

Markscheme

$- 11 \leqslant f(x) \leqslant 21$ A1A1

Note: A1 for correct end points, A1 for correct inequalities.

[2 marks]

${f^{ - 1}}(x) = \sqrt[3]{{\frac{{x - 5}}{2}}}$ (M1)A1

[2 marks]

$- 11 \leqslant x \leqslant 21,{\text{ }} - 2 \leqslant {f^{ - 1}}(x) \leqslant 2$ A1A1

[2 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2 - Core: Functions and equations » 2.1

Show 57 related questions

17N.1.hl.TZ0.11a: Determine whether ${f_n}$ is an odd or even function, justifying your answer.
17M.1.hl.TZ2.2b: Find an expression for ${f^{ - 1}}(x)$ .
17M.1.hl.TZ2.2a: Write down the range of $f$ .
17M.2.hl.TZ1.12e: Find the inverse function ${g^{ - 1}}$ and state its domain.
17M.2.hl.TZ1.12d: Explain why the inverse function ${f^{ - 1}}$ does not exist.
17M.2.hl.TZ1.12c: Explain why $f$ is an even function.
17M.2.hl.TZ1.12a: Find the largest possible domain $D$ for $f$ to be a function.
15N.2.hl.TZ0.12c: Consider the function defined by $h(x) = \frac{{2x - 5}}{{x + d}}$ , $x \ne - d$ and...
15N.2.hl.TZ0.12b: (i) Explain why $f$ does not have an inverse. (ii) The domain of $f$ is...
15N.2.hl.TZ0.12a: The functions $u$ and $v$ are defined as $u(x) = x - 3,{\text{ }}v(x) = 2x$ where...
15N.1.hl.TZ0.12d: Find the range of $f$ .
15N.1.hl.TZ0.12a: Show that $f$ is an odd function.
09M.1.hl.TZ2.11: A function is defined as $f(x) = k\sqrt x$ , with $k > 0$ and $x \geqslant 0$ . (a)...
12M.1.hl.TZ2.11b: Find an expression for the composite function $f \circ g(x)$ in the form...
12N.1.hl.TZ0.12d: (i) State ${F_n}(0){\text{ and }}{F_n}(1)$ . (ii) Show that ${F_n}(x) < x$ ,...
12N.1.hl.TZ0.12a: Find an expression for $(f \circ f)(x)$ .
12N.1.hl.TZ0.12c: Show that ${F_{ - n}}(x)$ is an expression for the inverse of ${F_n}$ .
08M.1.hl.TZ1.8: The functions f and g are defined...
08M.1.hl.TZ2.4: Let $f(x) = \frac{4}{{x + 2}},{\text{ }}x \ne - 2{\text{ and }}g(x) = x - 1$ . If...
11M.1.hl.TZ2.8: A function is defined by...
09N.1.hl.TZ0.4: Consider the function f , where $f(x) = \arcsin (\ln x)$ . (a) Find the domain of f...
SPNone.1.hl.TZ0.13c: Obtain expressions for the inverse function ${f^{ - 1}}$ and state their domains.
SPNone.1.hl.TZ0.5a: Determine whether f is even, odd or neither even nor odd.
13M.1.hl.TZ1.12d: Find the range of f.
13M.2.hl.TZ1.13d: (i) With f and g as defined in parts (a) and (b), solve $g \circ f(x) = 2$ . (ii) ...
10M.1.hl.TZ1.2: Shown below are the graphs of $y = f(x)$ and $y = g(x)$ . If...
10M.1.hl.TZ2.10: A function f is defined by $f(x) = \frac{{2x - 3}}{{x - 1}},{\text{ }}x \ne 1$ . (a) ...
10N.1.hl.TZ0.9: Consider the function $f:x \to \sqrt {\frac{\pi }{4} - \arccos x}$ . (a) Find the...
13M.1.hl.TZ2.12d: (i) Find an expression for ${f^{ - 1}}(x)$ . (ii) Sketch the graph of $y = f(x)$ ,...
11N.1.hl.TZ0.9b: Hence determine the range of the function $f:x \to \frac{{x + 1}}{{{x^2} + x + 1}}$ .
11N.1.hl.TZ0.9c: Explain why f has no inverse.
11N.2.hl.TZ0.8a: find ${f^{ - 1}}(x)$ , stating its domain;
12M.1.hl.TZ2.11c: (i) Find an expression for the inverse function ${f^{ - 1}}(x)$ . (ii) State the...
11M.1.hl.TZ1.10a: Find the largest possible domain of the function $g$ .
09N.2.hl.TZ0.9: (a) Given that the domain of $g$ is $x \geqslant a$ , find the least value of $a$ ...
11M.1.hl.TZ1.8b: Find the coordinates of the point where the graph of $y = f(x)$ and the graph of...
11M.1.hl.TZ1.8a: (i) Find $\left( {g \circ f} \right)\left( x \right)$ and write down the domain of the...
14M.2.hl.TZ1.12: Let $f(x) = \left| x \right| - 1$ . (a) The graph of $y = g(x)$ is drawn...
14M.1.hl.TZ2.14b: Find an expression for the composite function $h \circ g(x)$ and state its domain.
14M.1.hl.TZ2.14d: Nigel states that $f$ is an odd function and Tom argues that $f$ is an even...
14M.2.hl.TZ2.7b: Find the inverse function ${f^{ - 1}}$ , stating its domain.
15M.1.hl.TZ1.5b: Given that $g$ is an odd function, find the value of $r$ .
15M.1.hl.TZ1.9b: Find the range of $g \circ f$ .
15M.1.hl.TZ1.5a: Given that $f$ is an even function, show that $b = 0$ .
15M.1.hl.TZ1.5c: The function $h$ is both odd and even, with domain $\mathbb{R}$ . Find $h(x)$ .
15M.1.hl.TZ1.6a: Find an expression for ${f^{ - 1}}(x)$ .
15M.1.hl.TZ1.6b: Given that $f(x)$ can be written in the form $f(x) = A + \frac{B}{{2x - 1}}$ , find the...
15M.1.hl.TZ1.9a: Show that $g \circ f(x) = 3\sin \left( {2x + \frac{\pi }{5}} \right) + 4$ .
15M.1.hl.TZ1.9c: Given that $g \circ f\left( {\frac{{3\pi }}{{20}}} \right) = 7$ , find the next value of...
15M.1.hl.TZ2.10c: Find all values of $x$ for which $f(x) = {f^{ - 1}}(x)$ .
15M.1.hl.TZ2.11b: Hence show that $g \circ f(x) = \frac{{\sin x + \cos x}}{{\sin x - \cos x}}$ .
15M.1.hl.TZ2.13b: Hence show that $\sqrt 2 - 1 < \frac{1}{{\sqrt 2 }}$ .
15M.1.hl.TZ2.10b: Find an expression for ${f^{ - 1}}(x)$ .
15M.1.hl.TZ2.11a: Find an expression for $g \circ f(x)$ , stating its domain.
15M.1.hl.TZ2.13a: Show that $\frac{1}{{\sqrt n + \sqrt {n + 1} }} = \sqrt {n + 1} - \sqrt n$ where...
15M.2.hl.TZ1.6: A function $f$ is defined by...
14N.1.hl.TZ0.11a: (i) Find ${f^{ - 1}}(x)$ . (ii) State the domain of ${f^{ - 1}}$ .

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