Final answer:
The mathematical domain of the function A(x) = x^2 - 3 - 4 is x ∈ R, and the reasonable domain is x > 0.
Step-by-step explanation:
The mathematical domain of the function A(x) = x^2 - 3 - 4 represents all possible values of x for which the function is defined. In this case, since the function is a quadratic equation, its domain consists of all real numbers. Therefore, the mathematical domain is x ∈ R, where R represents the set of real numbers.
The reasonable domain, on the other hand, represents the values of x that make sense in the given context of the problem. In the context of the area of mirrors, it is reasonable to assume that the length of a mirror cannot be negative. Therefore, the reasonable domain is x > 0.
Comparing the mathematical and reasonable domains, we can conclude that the correct option is A) Mathematical: x∈R , Reasonable: x>0.