Question

find the domain of the logarithmic function.

f(x) = log (4 - x)

the domain of f(x) = log (4 - x) is
(type your answer in interval notation.)

Explanation:

Step1: Recall domain of logarithm

For \( \log(u) \), \( u > 0 \). Here \( u = 4 - x \), so \( 4 - x > 0 \).

Step2: Solve the inequality

Subtract 4: \( -x > -4 \). Multiply by -1 (reverse inequality): \( x < 4 \).
In interval notation, this is \( (-\infty, 4) \).

Answer:

\((-\infty, 4)\)