Question

Let f(x) = x^2 + 6 and g(x) = x+8/x . Find ( g o f)(­ -7)

Answer 1

Answer:
$\frac{63}{55}$

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) = $\frac{x+8}{x}$

Therefore:
(g o f)(x) = $\frac{x^2+6+8}{x^2+6} = \frac{x^2+14}{x^2+6}$

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) = $\frac{x^2+14}{x^2+6}$

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

Hope this helps :)

Answer 2

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.)