005 Sample Final A, Question 3 - Revision history

Matt Lee at 03:12, 22 May 2015

2015-05-22T03:12:46Z

Matt Lee at 03:12, 22 May 2015

2015-05-22T03:12:34Z

Matt Lee at 16:21, 8 May 2015

2015-05-08T16:21:37Z

Matt Lee: Created page with "'''Question ''' Find f $\circ$ g and its domain if $f(x) = x^2+1 \qquad g(x)=\sqrt{x-1}$ {| class="mw-collapsible mw-collapsed" style = "text-align:left..."

2015-05-01T04:07:16Z

Created page with "'''Question ''' Find f <math>\circ</math> g and its domain if <math>f(x) = x^2+1 \qquad g(x)=\sqrt{x-1}</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left..."

New page

'''Question ''' Find f <math>\circ</math> g and its domain if <math>f(x) = x^2+1 \qquad g(x)=\sqrt{x-1}</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answers
|-
|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>
|-
|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.
|-
|c) False. <math>y = x^2</math> does not have an inverse.
|-
|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
|-
|e) True.
|-
|f) False.
|}

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 |2) A point should be in the domain of f<math>\circ</math>g when it is in the domain of g, and g(x) is in the domain of f.
 |}
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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Step 1
+! Foundations:
 |-
 |First we find the domain of g. Since f <math>\circ</math> g = f(g(x)). So if x is not in the domain of g, it is not in the domain of f <math>\circ</math> g. The domain of g is <math>[1, \infty)</math>.
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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Step 2
+! Step 2:
 |-
 |To find f <math>\circ</math> g we replace any occurrence of x in f with g, to yield <math>(\sqrt{x - 1})^2 + 1 = x - 1 + 1 = x </math>
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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Final Answers:
 |-
 |f <math>\circ</math> g = <math> x </math>, and the domain is <math>[1, \infty)</math>.
 |}

005 Sample Final A, Question 3 - Revision history

Matt Lee at 03:12, 22 May 2015

Matt Lee at 03:12, 22 May 2015

Matt Lee at 16:21, 8 May 2015

Matt Lee: Created page with "'''Question ''' Find f \circ g and its domain if f(x) = x^2+1 \qquad g(x)=\sqrt{x-1} {| class="mw-collapsible mw-collapsed" style = "text-align:left..."

Matt Lee: Created page with "'''Question ''' Find f $\circ$ g and its domain if $f(x) = x^2+1 \qquad g(x)=\sqrt{x-1}$ {| class="mw-collapsible mw-collapsed" style = "text-align:left..."