To determine the domain of the function $f(x) = \frac{x - 2}{x + 10}$, we need to identify the values of $x$ for which the function is defined.

Since this is a rational function, it is undefined where the denominator is equal to zero. Thus, we set the denominator equal to zero and solve for $x$:

$x + 10 = 0$

$x = -10$

This tells us that the function is undefined at $x = -10$. Therefore, the domain of $f(x)$ includes all real numbers except $x = -10$.

Domain in Interval Notation

The domain of $f(x)$ is: $(-\infty, -10) \cup (-10, \infty)$

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Related Questions:

1. How would you find the range of a rational function?
2. What are common steps to simplify a rational function before finding its domain?
3. How do you determine vertical asymptotes in rational functions?
4. What other types of functions have restricted domains?
5. Can a rational function have a domain of all real numbers?

Tip:

When finding the domain of a rational function, always check where the denominator is zero, as this will indicate where the function is undefined.