Question

Let f(x) = x2 + 6 and g(x) = x + 8x . Find ( g o f)(­ -7)

Answer 1

Answer: $(gof)(-7) =495$

Step-by-step explanation:

Given the functions f(x) and g(x), to find $(gof)(x)$ you need to substitute $x=f(x)=x^2 + 6$ into the function g(x):

$(gof)(x) = ( x^2 + 6)+ 8( x^2 + 6)\\\\(gof)(x)=x^2 + 6+ 8x^2 + 48\\\\(gof)(x)=9x^2 + 54$

Now, to find  $(gof)(-7)$ you must substitute $x=-7$ into $(gof)(x)$, then you get:

$(gof)(-7) = 9(-7)^2 + 54\\\\(gof)(-7) =9(49)+54\\\\(gof)(-7) =441+54\\\\(gof)(-7) =495$