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]
