Respuesta :

altavistard
One way to approach this is to find (g o f)(x) first and then to replace x by -7:

g( f(x) ) = (x^2+6) + 8/(x^2+6)

Now replace x with -7.  We get:    ( g o f )(-7) = 49+6+8 / (49+6), or
                                                                        = 55 + 8 / 55, or 55 8/55 (ans.)
Louli
Answer:
[tex] \frac{63}{55} [/tex]

Explanation:
(g o f)(-7) is a composite function.
It means that we are going to substitute each x in the g function with f(x) and then substitute in the final expression with x = -7

Therefore, we will do this on two steps as follows:
1- getting (g o f)(x):
we have:
f (x) = x² + 6
g (x) = [tex] \frac{x+8}{x} [/tex]

Therefore:
(g o f)(x) = [tex] \frac{x^2+6+8}{x^2+6} = \frac{x^2+14}{x^2+6} [/tex]

2- getting (g o f)(-7):
We will simply substitute with x = -7 in the expression obtained from part 1 as follows:
(g o f)(x) = [tex] \frac{x^2+14}{x^2+6} [/tex]

(g o f)(x) = [tex] \frac{(-7)^2+14}{(-7)^2+6} [/tex] = [tex] \frac{63}{55} [/tex]

Hope this helps :)

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