Answer:The inverse of the h(x) is [tex]h^{-1}(x)=\frac{3x}{2}+2[/tex] Step-by-step explanation:Given : Expression [tex]h(x)=\frac{2x-4}{3}[/tex]To find : The inverse of the expression ?Solution : Expression [tex]h(x)=\frac{2x-4}{3}[/tex]Let, h(x)=y then [tex]y=\frac{2x-4}{3}[/tex]For inverse we replace the value of x and y and find the value of y in terms of x.Replace the value of x and y,[tex]x=\frac{2y-4}{3}[/tex]Solve for y by cross multiply,[tex]3x=2y-4[/tex]Adding 4 both side,[tex]3x+4=2y[/tex]Dividing by 2 both side,[tex]\frac{3x+4}{2}=y[/tex]Therefore, The inverse of the h(x) is [tex]h^{-1}(x)=\frac{3x}{2}+2[/tex]