It is given that the function g(x) is the inverse of f(x) so it follows:
[tex]g(x)=f^{-1}(x)[/tex]
It is given that f(-4)=9 so it follows:
[tex]\begin{gathered} f(-4)=9 \\ f^{-1}f(-4)=f^{-1}(9) \\ -4=g(9) \end{gathered}[/tex]
So the value of g(9)-3f(-4) is given by:
[tex]\begin{gathered} g(9)-3f(-4)=-4-3(9) \\ =-4-27 \\ =-31 \end{gathered}[/tex]
Hence the value is -31.
