Answer:
The inverse equation of
�
=
3
2
�
−
6
y=
2
3
x−6 is
�
=
2
3
�
+
4
x=
3
2
y+4.
Explanation:
To find the inverse of a function, interchange the roles of
�
x and
�
y and solve for the new
�
y. Start with the original equation:
�
=
3
2
�
−
6
y=
2
3
x−6
Now, interchange
�
x and
�
y:
�
=
3
2
�
−
6
x=
2
3
y−6
Solve for
�
y:
3
2
�
=
�
+
6
2
3
y=x+6
�
=
2
3
�
+
4
y=
3
2
x+4
So, the inverse equation is
�
=
2
3
�
+
4
x=
3
2
y+4.