Answer:
Inverse function: If a function f(x) is mapping x to y, then the inverse function of f(x) maps back y to x
Given that: [tex]y = \frac{2}{3}x -6[/tex]
Interchange the variable x and y;
[tex]x = \frac{2}{3}y -6[/tex]
Add 6 to both sides we get;
[tex]x +6= \frac{2}{3}y -6+6[/tex]
Simplify:
[tex]x+6= \frac{2}{3}y[/tex]
Multiply both sides by [tex]\frac{3}{2}[/tex] we get;
[tex]\frac{3}{2}(x+6) = y[/tex]
or
[tex]y = \frac{3}{2}x+ 9[/tex]
Therefore, the inverse of [tex]y = \frac{2}{3}x-6[/tex] is,
[tex]y = \frac{3}{2}x+ 9[/tex]
