Question

Plz answer hurry. 20 points for right answer

Answer 1

First, we need to define the function of (fog)(x)
(fog)(x) = f(g(x))
it means we need to substitute the x in the function f(x) with g(x)

f(x) = x + 7
change x with g(x)
fog(x) = g(x) + 7
fog(x) = $\cfrac{1}{x-13}$ + 7

equalize the denominators
fog(x) = $\cfrac{1}{x-13}$ + 7
fog(x) = $\cfrac{1}{x-13}+\cfrac{7(x-13)}{x-13}$

simplify
fog(x) = $\cfrac{7x-91+1}{x-13}$
fog(x) = $\cfrac{7x-90}{x-13}$

Second, determine the domain of the function
If the function is in fraction form, the denominator of the fraction can't be equal to zero.
x - 13 ≠ 0
x ≠ 13
The domain is {x| x≠13}
The answer is last option

Answer 2

Did You Figure This Out I Need Help Too. Lol