Question

find the domain of the logarithmic function.
f(x) = log (6 - x)

the domain of f(x) = log (6 - x) is .
(type your answer in interval notation.)

Explanation:

Step1: Recall log domain rule

For \( \log_b(u) \), \( u > 0 \). Here, \( u = 6 - x \), so \( 6 - x > 0 \).

Step2: Solve the inequality

Subtract 6: \( -x > -6 \). Multiply by -1 (reverse inequality): \( x < 6 \).

Step3: Write in interval notation

\( (-\infty, 6) \).

Answer:

\((-\infty, 6)\)