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

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

Answer: (A)

Verified step by step guidance

1. Identify the given equation: \(x + y = 7\). This represents a linear equation in two variables.
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 subtraction and addition are defined for all real numbers.
4. Therefore, the domain includes all real numbers, which can be written in interval notation as \(\left(-\infty, \infty\right)\).
5. Conclude that the function is defined for every real value of \(x\), so the domain is all real numbers.