# 005 Sample Final A, Question 4

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

Foundations:
1) How would you find the inverse for a simpler function like ${\displaystyle f(x)=3x+5}$?
Switch f(x) for y, to get ${\displaystyle y={\frac {3x}{2x-1}}}$, then switch y and x to get ${\displaystyle x={\frac {3y}{2y-1}}}$
${\displaystyle {\begin{array}{rcl}x&=&{\frac {3y}{2y-1}}\\x(2y-1)&=&3y\\2xy-x&=&3y\\2xy-3y&=&x\\y(2x-3)&=&x\\y&=&{\frac {x}{2x-3}}\end{array}}}$
${\displaystyle y={\frac {x}{2x-3}}}$