The domain of f(x) is the set of all real values except 7 , and the domain of g(x) is the set of all real values except -3. Witch of the following describes the domain of (g•f)(x)?

Answer: the domain of g [f(x) ] is the set of all real values except 7 and the x for which f(x) = - 3.

Explanation:

Taking (g•f)(x) as (g o f) (x), this is g (x) composed with f(x) you have this analysis.

(g o f) (x) is g [ f(x) ], which means that you first apply the function f and then apply the function g to the output of f(x).

The domain of g [ f(x) ] has to exclude 7, because it is not included in the domain of f(x).

Also the domain thas to exclude those values of x for which f(x) is - 3, because the domain of g(x) is the set of all real values except - 3.

So, the domain of g [f(x) ] is the set of all real values except 7 and the x for which f(x) = - 3.