Final answer:
-7 is in the domain of the composite function f°g because after applying g to -7, we obtain -14, which is within the domain of f.
Step-by-step explanation:
To determine if -7 is in the domain of the composite function f°g, we need to first find the function g(-7) and then see if that result can be an input to the function f(x).
The function g(x) = 3x + 7, so we calculate g(-7) by plugging -7 in place of x: g(-7) = 3(-7) + 7, which simplifies to g(-7) = -21 + 7 = -14.
Now, we need to see if -14 is a valid input for the function f(x) = x - 4. Since f(x) is defined for all real numbers, -14 is certainly in its domain. So, we conclude that -7 is in the domain of f°g because after applying g, we get a number (-14) that is in the domain of f.