Find the domain of the following function.
$x+y=7$

• A. $(-\infty ,\infty )$
• B. $[7,\infty )$
• C. $(-\infty ,7]$
• D. $(-\infty ,7)\cup (7,\infty )$

Answer: (A)

Verified step by step guidance

1. Identify the given equation: \(x + y = 7\). This represents a linear equation in two variables, \(x\) and \(y\).
2. Recall that the domain of a function is the set of all possible input values (usually \(x\)) for which the function is defined.
3. Since \(y\) can be expressed in terms of \(x\) as \(y = 7 - x\), there are no restrictions on \(x\) because any real number substituted for \(x\) will produce a corresponding \(y\) value.
4. Therefore, the domain includes all real numbers, which can be written in interval notation as \(\left(-\infty, \infty\right)\).
5. Conclude that the domain of the function defined by \(x + y = 7\) is all real numbers, meaning there are no values of \(x\) that are excluded.