Equations to find the inverse of f(x) = y = 3x/8+z

To find the inverse of the the function, it must be arranged in such a way that the independent variable be on the left side and the dependent variable on the right. So,f(x) = y = 3x/ (8 + x)y (8 + x) = 3x8y + xy = 3x8y = 3x - xy8y = x (3 - y)8y / (3-y) = xx = 8y / (3 -y)
Therefore,f-(x) = f(y) = x = 8y/ (3 - y)

I am not sure if your equation is
y=3x/(8+z) or y=(3x/8)+z

f(x)=y=3x/8 +z substitute x for y and y for x
x=3y/8 +z. Solve for y