It is a false proposition that the domain of function t = φ (x) is A and that of function y=f(t) is B, so the domain of compound function y = f [φ (x)] is A ∩ B.

For example, φ (x) = √ (1-x) domain x, f (x) = lnx domain x>0, and its composite function f [φ (x)] = ln √ (1-x) defines the domain X.

Another view is that the range of function t = φ (x) is C, and the domain of function y=f(t) is B, so the domain of compound function y = f [φ (x)] is C ∩ B, which is also a false proposition.

For example, φ (x) = x 2 takes the range y≥0, and f(x)=lnx defines the range x>0, and its compound function f [φ (x)] = lnx 2 defines the domain x≠0. Instead of x >；; 0。

"the domain of g and the domain of f are not empty sets" is a necessary condition for "function synthesis of g and f"

Because the domain of any function cannot be an empty set. In other words, there is no function whose domain is an empty set.

I suggest you read more counseling books and ask more questions about your study! ! Ha ha! !