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 domain of log function

For \( \log(u) \), \( u > 0 \). Here, \( u = 6 - x \). So, \( 6 - x > 0 \).

Step2: Solve the inequality

Subtract 6: \( -x > -6 \). Multiply by -1 (reverse inequality): \( x < 6 \).
In interval notation, this is \( (-\infty, 6) \).

Answer:

\((-\infty, 6)\)