To determine if the function is one-to-one, we can demonstrate if f(x) = f(y), so if x=y it is a one to one function
So:
[tex]\begin{gathered} 2x\text{ -}3=2y\text{ -}3 \\ 2x=\text{ }2y\text{ -}3\text{ +3} \\ 2x=2y \\ x=y \end{gathered}[/tex]
So it is a one-to-one function. Let's figure out the inverse. To do this we have to replace x with y, and then solve for y.
[tex]\begin{gathered} y=2x\text{ -}3 \\ x=2y\text{ -}3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ f^{\text{ -1}}(x)=\frac{\text{ }x+3}{2} \\ \end{gathered}[/tex]
