MathAdmin: Created page with " Find $f^{-1}(x)$ for $f(x) = \frac{3x-1}{4x+2}$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |..."

2015-06-01T05:46:19Z

Created page with "<span class="exam"> Find <math>f^{-1}(x)</math> for <math>f(x) = \frac{3x-1}{4x+2}</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |..."

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<span class="exam"> Find <math>f^{-1}(x)</math> for <math>f(x) = \frac{3x-1}{4x+2}</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
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| How would you find the inverse for a simpler function like <math>f(x)=2x+4?</math>
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|Answer:
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|You would replace <math>f(x)</math> with <math>y</math>. Then, switch <math>x</math> and <math>y</math>. Finally, we would solve for <math>y</math>.
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Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
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|We start by replacing <math>f(x)</math> with <math>y</math>.
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|This leaves us with <math>y=\frac{3x-1}{4x+2}</math>
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
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|Now, we swap <math>x</math> and <math>y</math> to get <math>x=\frac{3y-1}{4y+2} </math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
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|Starting with <math>x=\frac{3y-1}{4y+2} </math>, we multiply both sides by <math>4y+2</math> to get
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|<math>x(4y+2)=3y-1</math>.
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|Now, we need to get all the <math>y</math> terms on one side. So, adding <math>1</math> and <math>-4xy</math> to both sides we get
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|<math> 2x+1=3y-4xy</math>.
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 4:
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|Factoring out <math>y</math>, we get <math> 2x+1=y(3-4x) </math>. Now, dividing by <math>(3-4x)</math>, we get
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|<math>\frac{2x+1}{3-4x}=y</math>. Replacing <math>y</math> with <math>f^{-1}(x)</math>, we arrive at the final answer
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|<math>f^{-1}(x)=\frac{2x+1}{3-4x}</math>
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
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|<math>f^{-1}(x)=\frac{2x+1}{3-4x}</math>
|}

[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 1 - Revision history

MathAdmin: Created page with " Find f^{-1}(x) for f(x) = \frac{3x-1}{4x+2} {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |..."

MathAdmin: Created page with " Find $f^{-1}(x)$ for $f(x) = \frac{3x-1}{4x+2}$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |..."