Question

find the domain of the function and express the domain in interval notation.
\\( y = \log(7 - x) \\)
the domain is \\( \square \\).
(\\(\square,\square\\)) \\(\square,\square\\) (\\(\square,\square\\)
\\(\square,\square\\)) \\(\infty\\) \\(-\infty\\)
\\(\frac{\square}{\square}\\)

Explanation:

Step1: Recall log domain rule

For \( y = \log(u) \), \( u > 0 \). Here, \( u = 7 - x \), so \( 7 - x > 0 \).

Step2: Solve the inequality

Subtract 7: \( -x > -7 \). Multiply by -1 (reverse inequality): \( x < 7 \).

Step3: Write in interval notation

All real numbers less than 7: \( (-\infty, 7) \).

Answer:

\((-\infty, 7)\)