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:
![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}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B3%2Ax-15%7D%7B2%7D%20%5C%5Cf%28x%29%3Dy%5C%5C%5C%5Cy%3D%5Cfrac%7B3%2Ax-15%7D%7B2%7D%5C%5C%202%2Ay%3D3%2Ax-15%5C%5C3%2Ax%3D2%2Ay%2B15%5C%5Cx%3D%5Cfrac%7B2%2Ay%2B15%7D%7B3%7D)
Then, we have to change the variables to the next form:
![x=f^-^1(x)\\y=x](https://tex.z-dn.net/?f=x%3Df%5E-%5E1%28x%29%5C%5Cy%3Dx)
Finally, the inverse function is:
![f^-^1(x)=\frac{2*x+15}{3}](https://tex.z-dn.net/?f=f%5E-%5E1%28x%29%3D%5Cfrac%7B2%2Ax%2B15%7D%7B3%7D)
I have <u>attached an image</u> with the <em>sequence of steps</em>: