The function given in the image is:

$f(x) = -7x + 5$

This is a linear function, and linear functions are defined for all real values of $x$. Since there are no restrictions such as division by zero or taking the square root of a negative number, the domain of this function is all real numbers.

In interval notation, the domain is:

$(-\infty, \infty)$

Would you like any further details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the range of a linear function like $f(x) = -7x + 5$?
2. How would the domain change if the function were $f(x) = \frac{1}{x}$?
3. Can a linear function ever have a restricted domain? Under what conditions?
4. How does the slope of the function $-7x$ affect its graph?
5. What is the x-intercept of the function $f(x) = -7x + 5$?

Tip: Always remember that linear functions have an unrestricted domain, but if you encounter square roots or denominators, check for restrictions.