The given function is
[tex]f(x)=2x-3[/tex]The expression f(x)=9 means that we have to replace it for 9 and solve for x.
[tex]9=2x-3[/tex]We add 3 on each side.
[tex]\begin{gathered} 9+3=2x-3+3 \\ 12=2x \end{gathered}[/tex]Then, we divide the equation by 2.
[tex]\begin{gathered} \frac{2x}{2}=\frac{12}{2} \\ x=6 \end{gathered}[/tex]