Difference between revisions of "005 Sample Final A, Question 4"

Latest revision as of 20:16, 21 May 2015

Question Find the inverse of the following function $f(x)={\frac {3x}{2x-1}}$

Foundations:
1) How would you find the inverse for a simpler function like $f(x)=3x+5$ ?
Answer:
1) you would replace f(x) by y, switch x and y, and finally solve for y.

Step 1:
Switch f(x) for y, to get $y={\frac {3x}{2x-1}}$ , then switch y and x to get $x={\frac {3y}{2y-1}}$

Step 2:
Now we have to solve for y: ${\begin{array}{rcl}x&=&{\frac {3y}{2y-1}}\\x(2y-1)&=&3y\\2xy-x&=&3y\\2xy-3y&=&x\\y(2x-3)&=&x\\y&=&{\frac {x}{2x-3}}\end{array}}$

Final Answer:
$y={\frac {x}{2x-3}}$

@@ Line 1: / Line 1: @@
 '''Question''' Find the inverse of the following function <math> f(x) = \frac{3x}{2x-1}</math>
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Foundations:
+|-
+|1) How would you find the inverse for a simpler function like <math>f(x) = 3x + 5</math>?
+|-
+|Answer:
+|-
+|1) you would replace f(x) by y, switch x and y, and finally solve for y.
+|}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 11: / Line 24: @@
 |-
 | Now we have to solve for y:
-<math> \begin{array}{rcl}
+::<math> \begin{array}{rcl}
 x & = & \frac{3y}{2y-1}\\
 x(2y - 1) & = & 3y\\
@@ Line 18: / Line 31: @@
 y(2x - 3) & = & x\\
 y & = & \frac{x}{2x - 3}
-</math>
+\end{array}</math>
+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Final Answer:
+|-
+|<math> y = \frac{x}{2x-3}</math>
 |}