we have the following:
[tex]\begin{gathered} f\left(x\right)=2x+1 \\ y=2x+1 \end{gathered}[/tex]the inverse would be:
[tex]\begin{gathered} x=2y+1 \\ 2y=x-1 \\ y=\frac{x-1}{2} \\ y=\frac{1}{2}x-\frac{1}{2} \end{gathered}[/tex]The answer is the first option