[tex]y=\frac{2x}{2-3x}[/tex]
1) The best way to tackle this question is by plotting the graph of this function and then performing the horizontal line test.
So let's sketch out the following function:
Note that this function is a one-to-one function for a horizontal line hits the graph only once.
2) Since, invertible functions can only come from Bijective functions (one-to-one and surjective functions simultaneously) then we can write out this and find the inverse of that inverse function, swapping the variables and then isolating the x on the left side
[tex]\begin{gathered} y=\frac{2x}{2+3x} \\ x=\frac{2y}{2+3y} \\ 2y=(2+3y)x \\ 2y=2x+3yx \\ -3yx+2y=2x \\ y(-3x+2)=2x \\ \frac{y(-3x+2)}{(-3x+2)}=\frac{2x}{(-3x+2)} \\ y=\frac{2x}{2-3x} \\ \end{gathered}[/tex]
