If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = x[/tex]
which means
[tex]2f^{-1}(x)+3 = x[/tex]
Solve for [tex]f^{-1}(x)[/tex] :
[tex]2f^{-1}(x) + 3 = x \\\\ 2f^{-1}(x) = x - 3 \\\\ f^{-1}(x) = \dfrac{x-3}2 = \boxed{\dfrac12x-\dfrac32}[/tex]
