The domain of a function refers to the set of possible input values (typically represented by x) for which the function is defined. While many functions can take any real number as an input, there are instances where the domain is restricted.
For example, a function like f(x) = 1/x is not defined for x = 0 because division by zero is undefined. Therefore, the domain of this function is all real numbers except zero, which can be expressed in interval notation as (-∞, 0) ∪ (0, ∞).
Similarly, functions involving square roots, such as g(x) = √x, are only defined for non-negative x (i.e., x ≥ 0). Here, the domain is [0, ∞).
In general, to determine if a function’s domain includes all real numbers, one should check the operations involved (like division or square roots) and identify any values that would lead to undefined expressions or violations of the function’s definition.