Question

Determine the domain of the function. (1 point) ( f(x) = 4/x² )

a) All real numbers except x = 0
b) All real numbers except x = 2
c) All real numbers except x = -2
d) All real numbers except x = 0 and x = 2

Answer 1

The domain of the function f(x) = 4/x² is all real numbers except x = 0, as this is the only value for which the function is undefined.

Step-by-step explanation:

The domain of a function is the set of all possible inputs (values of x) for which the function is defined. For the given function f(x) = 4/x², the function is defined for all real numbers except where the denominator equals zero, as division by zero is undefined. Since x² equals zero only when x is zero, the only value that cannot be in the domain is x = 0. Therefore, the correct option for the domain of the function f(x) is all real numbers except x = 0. This does not change regardless of any restrictions like 0 ≤ x ≤ 20, as those are constraints on the domain, not determinants of where the function is undefined.