Answer:
(f∘g)(x) = 7/(x+7)
domain: (-∞, -7) ∪ (-7, 0) ∪ (0, ∞)
Step-by-step explanation:
(f∘g)(x) = f(g(x)) = (7/x)/((7/x) +1) . . . . substitute g(x) for x in the definition of f(x)
... = 7/(x(7/x) +1)
... (f∘g)(x) = 7/(7 +x)
The domain may not include any values of x that make any of the function values become undefined. That is, denominator values of zero are not allowed.
For x=0, g(x) is undefined.
For x=-7, (f∘g)(x) is undefined.
Thus the domain is all real numbers except -7 or 0.
