Question

find the domain of the logarithmic function.
f(x) = log (3 - x)

the domain of f(x) = log (3 - x) is .
(type your answer in interval notation.)

Explanation:

Step1: Recall domain of logarithm

For a logarithmic function \( \log(u) \), the argument \( u \) must be positive, i.e., \( u>0 \).
Here, \( u = 3 - x \), so we set \( 3 - x>0 \).

Step2: Solve the inequality

Solve \( 3 - x>0 \) for \( x \).
Subtract 3 from both sides: \( -x > - 3 \).
Multiply both sides by -1 (remember to reverse the inequality sign): \( x < 3 \).

Step3: Write in interval notation

The solution \( x < 3 \) in interval notation is \( (-\infty, 3) \).

Answer:

\((-\infty, 3)\)