To find the domain of the function $f(x) = \frac{x+2}{x-2}$, we need to determine the values of $x$ for which the function is defined. The function is undefined when the denominator is equal to zero because division by zero is not allowed.

Steps to find the domain:

1. Identify the denominator: The denominator of the function is $x - 2$.

2. Set the denominator equal to zero and solve for $x$: $x - 2 = 0$ $x = 2$ So, the function is undefined when $x = 2$.

3. State the domain: The domain of the function $f(x) = \frac{x+2}{x-2}$ includes all real numbers except $x = 2$.

Conclusion:

The domain of $f(x) = \frac{x+2}{x-2}$ is: $\boxed{x \in \mathbb{R}, x \neq 2}$

Would you like further details or have any questions?

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Related Questions:

1. What is the range of $f(x) = \frac{x+2}{x-2}$?
2. How do you find the vertical asymptotes of a rational function?
3. Can you find the horizontal asymptote of $f(x) = \frac{x+2}{x-2}$?
4. How do you graph $f(x) = \frac{x+2}{x-2}$?
5. What happens to $f(x)$ as $x$ approaches 2 from the left and right?

Tip: When finding the domain of a function, always look for values that make the denominator zero, as these points will be excluded from the domain.