Question

Find the domain of the logarithmic function.  
f left parenthesis x right parenthesis equals log left parenthesis 14 minus x right parenthesis
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Part 1
The domain of f left parenthesis x right parenthesis equals log left parenthesis 14 minus x right parenthesis is
  
enter your response here.
​(Type your answer in interval​ notation.)

Answer 1

To find the domain of the function \( f(x) = \log(14 - x) \), we need to determine the values of \( x \) for which the argument of the logarithm is positive. Specifically, we require:

\[
14 - x > 0
\]

Solving this inequality, we add \( x \) to both sides:

\[
14 > x
\]

or equivalently,

\[
x < 14
\]

Additionally, there is no restriction on how low \( x \) can go, so we have:

\[
x \in (-\infty, 14)
\]

Thus, the domain of \( f(x) \) in interval notation is:

\[
\boxed{(-\infty, 14)}
\]