f(x) = 3x/(8+x) = y
f^(-1) is the inverse function. As its name suggests if f(x) = y that we need to find a g(x) such that g(y) = x
In order to find f^(-1) switch x with y and solve for y
3y/(8+y) = x
x(8+y) = 3y
8x+xy = 3y
8x=3y-xy
8x = y(3-x)
y = 8x/(3-x)
f^(-1) = y = 8x/(3-x)