Answer:
[tex](fog)(x)=x^2+12x+36[/tex]
[tex](gof)(x)=x^2+6[/tex]
[tex](fog)(-3)=9[/tex]
[tex](gof)(-3)=15[/tex]
Step-by-step explanation:
[tex]f(x)=x^2[/tex]
[tex]g(x)=x+6[/tex]
[tex](fog)(x)= f(g(x))[/tex]
Plug in g(x)
[tex](fog)(x)= f(g(x))=f(x+6)[/tex]
replace x+6 for x in f(x)
[tex](fog)(x)= f(g(x))=f(x+6)=(x+6)^2=x^2+12x+36[/tex]
[tex](fog)(x)=x^2+12x+36[/tex]
[tex](gof)(x)= g(f(x))[/tex]
[tex](gof)(x)= g(f(x))=g(x^2)=x^2+6[/tex]
[tex](gof)(x)=x^2+6[/tex]
[tex](fog)(-3)=(-3)^2+12(-3)+36=9[/tex]
[tex](gof)(-3)=(-3)^2+6=15[/tex]
