Compute the inverse of one function and see if it matches the other. I'll pick f.
[tex]x=18-3y[/tex]
[tex]y=\frac{x-18}{-3}[/tex]
[tex]f^{-1}(x)=6-\frac{x}{3}=g(x)[/tex]
This also means that [tex]g^{-1}(x)=f(x)[/tex] so the functions are inverse.
Hope this helps :)
