Question

At a grocery store, apples cost $2 per pound and oranges cost $3.50 per pound. The function representing the total cost, in dollars, for x pounds of apples and x pounds of oranges is f(x) = 5.5x. How does the mathematical domain of the function compare to the reasonable domain?

Answer 1

The reasonable domain is a proper subset of the mathematical domain.

Explanation:

The domain of a function is the set for which the function is defined. We have that
`f(x) = 5.5x` consists of multypling the input by a factor of 5.5. This operation can be done with any type of number, so the domain of the function is the set of real numbers. However, in the context of the problem, it doesn't make sense to have negative values of x,since x represents a weight of apples and oranges. Then, in the context of the problem
`x\geq 0`. So the reasonable domain of the function is the set of real numbers that are greater or equal to zero. In this case, the reasonable domain is proper subset of the mathematical domain, since they are obviously not equal (hence it is a proper subset).