005 Sample Final A, Question 4

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

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: Failed to parse (unknown function "\begin{array}"): {\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} }