Answer: [tex](gof)(-7) =495[/tex]
Step-by-step explanation:
Given the functions f(x) and g(x), to find [tex](gof)(x)[/tex] you need to substitute [tex]x=f(x)=x^2 + 6[/tex] into the function g(x):
[tex](gof)(x) = ( x^2 + 6)+ 8( x^2 + 6)\\\\(gof)(x)=x^2 + 6+ 8x^2 + 48\\\\(gof)(x)=9x^2 + 54[/tex]
Now, to find [tex](gof)(-7)[/tex] you must substitute [tex]x=-7[/tex] into [tex](gof)(x)[/tex], then you get:
[tex](gof)(-7) = 9(-7)^2 + 54\\\\(gof)(-7) =9(49)+54\\\\(gof)(-7) =441+54\\\\(gof)(-7) =495[/tex]
