Answer:
The answer is the attached image
Step-by-step explanation:
In order to determine the inverse of any function, we have to think that the independent variable is "y" instead of "x".
So, firstly we have to free the "x" variable:
[tex]f(x)=\frac{3*x-15}{2} \\f(x)=y\\\\y=\frac{3*x-15}{2}\\ 2*y=3*x-15\\3*x=2*y+15\\x=\frac{2*y+15}{3}[/tex]
Then, we have to change the variables to the next form:
[tex]x=f^-^1(x)\\y=x[/tex]
Finally, the inverse function is:
[tex]f^-^1(x)=\frac{2*x+15}{3}[/tex]
I have attached an image with the sequence of steps:
