gof means that we must first evalute f at x and next evalute the result in g.
In our case,
[tex]\text{gof(x)}=g(f(x))[/tex]
By taking into account that f(x)=3x-1 and g(x)=4x^2+9, we have
[tex]\begin{gathered} (\text{gof)(x)}=g(f(x)=g(3x-1)=4(3x-1)^2+9 \\ \end{gathered}[/tex]
In summary,
[tex](\text{gof)(x)}=4(3x-1)^2+9[/tex]
Now, we must substitute x=-2 in this lat equation, It yields
[tex](\text{gof)(-}2)=4(3(-2)-1)^2+9[/tex]
hence, we obtain,
[tex]\begin{gathered} (\text{gof)(-}2)=4(-6-1)^2+9 \\ (\text{gof)(-}2)=4(-7)^2+9 \\ (\text{gof)(-}2)=4\cdot49+9 \\ (\text{gof)(-}2)=196+9 \\ (\text{gof)(-}2)=205 \end{gathered}[/tex]
Hence, the answer is 205
