Let f (x) = x^2+5 and g (x) = x+5/x. Find (g fog f) (-3).

A:1/4

B:14/19

C:19/14

D:49/9

For this case we have the following functions:

f (x) = x ^ 2 + 5

g (x) = x + 5 / x

Doing the composition of functions we have:

(fog) (x) = ((x + 5) / x) ^ 2 + 5

Evaluating for x = - 3 we have:

(fog) ( - 3) = ((-3 + 5) / - 3) ^ 2 + 5

(fog) ( - 3) = (2 / - 3) ^ 2 + 5

(fog) ( - 3) = (4/9) + 5

(fog) ( - 3) = (4 + 45) / (9)

(fog) ( - 3) = (49) / (9)

Answer:

D: 49/9