Answer:
[tex]\large\boxed{f^{-1}(x)=y=\dfrac{x}{2}-\dfrac{3}{2}\to f^{-1}(x)=\dfrac{1}{2}x-\dfrac{3}{2}}[/tex]
Step-by-step explanation:
[tex]f(x)=2x+3\to y=2x+3\\\\\text{exchange x to y and vice versa:}\\\\x=2y+3\\\\\text{solve for}\ y:\\\\2y+3=x\qquad\text{subtract 3 from both sides}\\\\2y=x-3\qquad\text{divide both sides by 2}\\\\y=\dfrac{x}{2}-\dfrac{3}{2}[/tex]
