004 Sample Final A, Problem 1 - Revision history

Kayla Murray at 04:08, 29 April 2015

2015-04-29T04:08:01Z

2015-04-29T04:07:45Z

2015-04-29T02:26:11Z

2015-04-29T02:25:31Z

2015-04-29T02:24:07Z

2015-04-29T02:23:16Z

2015-04-29T01:56:19Z

2015-04-28T21:25:54Z

@@ Line 4: / Line 4: @@
 ! Foundations
 |-
-| How would you find the inverse for a simpler function like <math>f(x)=2x+4</math>?
+| How would you find the inverse for a simpler function like <math>f(x)=2x+4?</math>
 |-
 |Answer:

@@ Line 4: / Line 4: @@
 ! Foundations
 |-
-| How would you find the inverse for a simpler function like <math>f(x)=2x+4</math>
+| How would you find the inverse for a simpler function like <math>f(x)=2x+4</math>?
 |-
 |Answer:

@@ Line 35: / Line 35: @@
 |<math>x(4y+2)=3y-1</math>.
 |-
-|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
+|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
 |-
 |<math> 2x+1=3y-4xy</math>.

@@ Line 35: / Line 35: @@
 |<math>x(4y+2)=3y-1</math>.
 |-
-|Now, we need to get all the <math>y</math> terms on one side. So, adding 1 and <math>-4xy</math> to both sides we get
+|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
 |-
 |<math> 2x+1=3y-4xy</math>.

@@ Line 17: / Line 17: @@
 ! Step 1:
 |-
-|We start by replacing <math>f(x)</math> with <y>.
+|We start by replacing <math>f(x)</math> with <math>y</math>.
 |-
 |This leaves us with <math>y=\frac{3x-1}{4x+2}</math>

@@ Line 4: / Line 4: @@
 ! Foundations
 |-
+| How would you find the inverse for a simpler function like <math>f(x)=2x+4</math>
 |-
+|Answer:
 |-
-|Answers:
+|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>.
 |}
@@ Line 21: / Line 17: @@
 ! Step 1:
 |-
+|We start by replacing <math>f(x)</math> with <y>.
 |-
+|This leaves us with <math>y=\frac{3x-1}{4x+2}</math>
 |}
@@ Line 29: / Line 25: @@
 ! Step 2:
 |-
+|Now, we swap <math>x</math> and <math>y</math> to get <math>x=\frac{3y-1}{4y+2} </math>.
 |}
@@ Line 37: / Line 31: @@
 ! Step 3:
 |-
+|Starting with <math>x=\frac{3y-1}{4y+2} </math>, we multiply both sides by <math>4y+2</math> to get
 |-
+|<math>x(4y+2)=3y-1</math>.
 |-
+|Now, we need to get all the <math>y</math> terms on one side. So, adding 1 and <math>-4xy</math> to both sides we get
 |}
@@ Line 47: / Line 43: @@
 ! Step 4:
 |-
+|Factoring out <math>y</math>, we get <math> 2x+1=y(3-4x) </math>. Now, dividing by <math>(3-4x)</math>, we get
 |-
+|<math>f^{-1}(x)=\frac{2x+1}{3-4x}</math>
 |}
@@ Line 55: / Line 53: @@
 ! Final Answer:
 |-
+|<math>f^{-1}(x)=\frac{2x+1}{3-4x}</math>
 |}
 [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

← Older revision		Revision as of 01:56, 29 April 2015
Line 1:		Line 1:
	<span class="exam"> Find <math>f^{-1}(x)</math> for <math>f(x) = \frac{3x-1}{4x+2}</math>		<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
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|Answers:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+
		+	Solution:
		+
		+	{\| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 1:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 2:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 3:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 4:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Final Answer:
		+	\|-
		+	\|
		+	\|}
		+
		+	[[004 Sample Final A\|<u>'''Return to Sample Exam</u>''']]

← Older revision		Revision as of 21:25, 28 April 2015
Line 1:		Line 1:
−	Find <math>f^{-1}(x)</math> for <math ~~style = "vertical-align: -17%;~~>f(x) = \frac{3x-1}{4x+2}</math>	+	<span class="exam"> Find <math>f^{-1}(x)</math> for <math>f(x) = \frac{3x-1}{4x+2}</math>