Question

find the domain of the logarithmic function. f(x) = log (12 - x) the domain of f(x) = log (12 - x) is \boxed{}. (type your answer in interval notation.)

Explanation:

Step1: Recall domain of log function

The argument of a logarithmic function \( \log(u) \) must be positive, so \( u > 0 \).
For \( f(x)=\log(12 - x) \), set \( 12 - x>0 \).

Step2: Solve the inequality

Solve \( 12 - x>0 \). Subtract 12 from both sides: \( -x > - 12 \). Multiply both sides by - 1 (remember to reverse the inequality sign): \( x < 12 \).

Step3: Write in interval notation

In interval notation, \( x < 12 \) is \( (-\infty, 12) \).

Answer:

\((-\infty, 12)\)