Functions: Domain - log function - Numbas at mathcentre.ac.uk

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Ruth Hand

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2 years, 9 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

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Ruth Hand 2 years, 9 months ago

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Ruth Hand 4 years, 7 months ago

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Question statement

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			Name	Type	Generated Value

out	expression	q
inp	expression	w
num	list	[ 10, 9 ]
n	integer	3
c	list	List of 24 items
rat	string	\[\simplify{{out}({inp})=({num
a	integer	-1
b	integer	2
base	integer	3
d	integer	9

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expression(random('f','h','g','p','q','y'))

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Given that

$g(t)=\log_{\var{base}}(\simplify{t-{c[0]}}),$ what do we require of

$t$ so that

$g(t)$ is defined as a function?

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$t>\var{c[0]}$

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$t\ge \var{c[0]}$

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$t<\var{c[0]}$

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$t\le \var{c[0]}$

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$t>0$

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$t\ne0$

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Advice

For a function such as

$g(t)=\log_{\var{base}}(\simplify{t-{c[0]}})$

we can only take the log of a positive number. That is,

$\simplify{t-{c[0]}>0} .$

Rearranging this inequality for $t$ gives $\simplify{t>{c[0]}}$ .

Therefore,

$\text{Domain}(g)=\{t\in\mathbb{R}:\,\simplify{t>{c[0]}}\}.$

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This question is used in the following exams:

All the good stuff by Chris Templet in Chris's workspace.
EGD125_Quiz1 by Matt Falk in Matt's workspace.
Test 2 - inter-related topics by Emma Coutts in SQA Higher Diagnostic Test.

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Functions: Domain - log function

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Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 2 years, 9 months ago

Ruth Hand 4 years, 7 months ago

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Functions: Domain - log function

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Taxonomy: mathcentre

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Taxonomy: Context

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Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 2 years, 9 months ago

Ruth Hand 4 years, 7 months ago

Error in variable testing condition

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