[tex]f(x)=2x-3\to y=2x-3\\\\\text{exchange x and y}\\\\x=2y-3\\\\\text{solve for y}\\\\2y-3=x\qquad\text{add 3 to both sides}\\\\2y=x+3\qquad\text{divide both sides by 2}\\\\y=\dfrac{1}{2}x+\dfrac{3}{2}\\\\Answer:\ \boxed{f^{-1}(x)=\dfrac{1}{2}x+\dfrac{3}{2}}[/tex]
