Difference between revisions of "005 Sample Final A, Question 2"

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(Created page with "'''Question''' Find the domain of the following function. Your answer should be in interval notation <math> f(x) = \frac{1}{\sqrt{x^2-x-2}}</math> <br> {| class="mw-collapsib...")
 
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! Final Answers
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! Foundations:
 
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|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
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|1) What is the domain of <math>\frac{1}{\sqrt{x}}</math>?
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|2) How can we factor <math>x^2 - x - 2</math>?
 
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|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
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| Answer:
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|1) The domain is <math>(0, \infty)</math>. The domain of <math>\frac{1}{x}</math> is <math>[0, \infty)</math>, but we have to remove zero from the domain since we cannot divide by 0.
 
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|c) False. <math>y = x^2</math> does not have an inverse.
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|2) <math>x^2 - x -2 = (x - 2)(x - 1)</math>
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|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
 
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|e) True.
 
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|f) False.
 
 
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Revision as of 08:56, 6 May 2015

Question Find the domain of the following function. Your answer should be in interval notation

Foundations:
1) What is the domain of ?
2) How can we factor Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 - x - 2} ?
Answer:
1) The domain is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (0, \infty)} . The domain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{x}} is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [0, \infty)} , but we have to remove zero from the domain since we cannot divide by 0.
2) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 - x -2 = (x - 2)(x - 1)}
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