The text from the image translates as follows:

"Write the domain of the function $f(x) = \log(5 - x)$ using appropriate interval notation. For example: $(0,1]$, $[0,1)$, or $(-\infty, \infty)$. You can copy the symbol $\infty$ from here or use the symbol $L$ instead."

Solution:

The function given is $f(x) = \log(5 - x)$. To determine the domain of this function, we must ensure that the argument of the logarithmic function is strictly positive because the logarithm of a non-positive number is undefined in the real number system.

So, we need: $5 - x > 0$ $x < 5$

Thus, the domain of the function is all values of $x$ less than 5. In interval notation, the domain is:

$(-\infty, 5)$

Final answer:

The domain of the function is $(-\infty, 5)$.

Would you like more details or have any questions?

Here are five related questions to expand this topic:

1. What would be the domain of the function $f(x) = \log(x + 2)$?
2. How does the domain change if the logarithm base changes, like in $f(x) = \log_2(5 - x)$?
3. What is the range of the function $f(x) = \log(5 - x)$?
4. How do you determine the domain of a logarithmic function that involves multiple variables, such as $f(x) = \log(5 - x^2)$?
5. Can you explain how the domain of logarithmic functions relates to the properties of exponential functions?

Tip: Always remember that the argument of a logarithmic function must be positive for real numbers. This principle helps in finding the domain efficiently!