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

Revision as of 09:56, 6 May 2015

Question Find the domain of the following function. Your answer should be in interval notation $f(x)={\frac {1}{\sqrt {x^{2}-x-2}}}$

Foundations:
1) What is the domain of ${\frac {1}{\sqrt {x}}}$ ?
2) How can we factor $x^{2}-x-2$ ?
Answer:
1) The domain is $(0,\infty )$ . The domain of ${\frac {1}{x}}$ is $[0,\infty )$ , but we have to remove zero from the domain since we cannot divide by 0.
2) $x^{2}-x-2=(x-2)(x-1)$

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Foundations:
 |-
-|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>
+|1) What is the domain of <math>\frac{1}{\sqrt{x}}</math>?
+|-
+|2) How can we factor <math>x^2 - x - 2</math>?
 |-
-|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.
+| Answer:
+|-
+|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.
 |-
-|c) False. <math>y = x^2</math> does not have an inverse.
+|2) <math>x^2 - x -2 = (x - 2)(x - 1)</math>
-|-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
-|-
-|e) True.
-|-
-|f) False.
 |}