Difference between revisions of "004 Sample Final A, Problem 1"

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! Foundations
 
! 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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! Step 1:
 
! 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>
 
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! Step 2:
 
! 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>.
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! Step 3:
 
! 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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! Step 4:
 
! 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>
 
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! Final Answer:
 
! Final Answer:
 
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|<math>f^{-1}(x)=\frac{2x+1}{3-4x}</math>
 
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]
 
[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 21:08, 28 April 2015

Find for

Foundations
How would you find the inverse for a simpler function like
Answer:
You would replace with . Then, switch and . Finally, we would solve for .


Solution:

Step 1:
We start by replacing with .
This leaves us with
Step 2:
Now, we swap and to get .
Step 3:
Starting with , we multiply both sides by to get
.
Now, we need to get all the terms on one side. So, adding and to both sides we get
.
Step 4:
Factoring out , we get . Now, dividing by , we get
. Replacing with , we arrive at the final answer
Final Answer:

Return to Sample Exam

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