Final answer:
The domain of a function is the set of all valid input values. Given f(x) = 1 and g(x) = x^2 - 4, since both functions can accept any real numbers their domains are all real numbers. Therefore, the domain of the composite function (gºf)(x) is all real numbers.
Step-by-step explanation:
In Mathematics, the domain of a function refers to the set of all possible input values (x-values) that will give valid output values. In the case of the function composition (gºf)(x), the domain is influenced by the domain of both function f and function g.
Given the functions f(x) = 1 and g(x) = x^2 - 4, the first function f(x) = 1 can accept any real number as its input, hence its domain is all real numbers. Looking to g(x) = x^2 - 4, you can also see that any real number can be squared and have 4 subtracted from it, so its domain is also all real numbers.
Therefore, following the above, we can say the domain of the composite function (gºf)(x) is also all real numbers.
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