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) = [tex] \cfrac{1}{x-13} [/tex] + 7
equalize the denominators
fog(x) = [tex] \cfrac{1}{x-13} [/tex] + 7
fog(x) = [tex]\cfrac{1}{x-13}+\cfrac{7(x-13)}{x-13}[/tex]
simplify
fog(x) = [tex] \cfrac{7x-91+1}{x-13} [/tex]
fog(x) = [tex] \cfrac{7x-90}{x-13} [/tex]
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
