Why is a functions denominator the domain of the function?
The limits on the domain, due to the denominator, are imposed, because one must not attempt do divide by zero; it is an undefined operation. Let’s consider the function: f(x) = (x + 1)/(x – 2) If one follows the rule that the denominator must not become zero, then one must write the following restriction on the above function: (x – 2) ≠ 0 In mathematical notation one would put a semicolon after the function and then write the restriction after the semicolon as follows: f(x) = (x + 1)/(x – 2); (x – 2) ≠ 0 However, one should simplify the inequality, before writing the restriction as follows: (x – 2) ≠ 0 (x – 2) + 2 ≠ 0 + 2 x ≠ 2 This really states that the domain of the function is; “You can pick any number for x that you want, except 2”. Mathematicians would write this as follows: f(x) = (x + 1)/(x – 2); x ≠ 2 I hope that this answers your question.
