Find the domain of the function \( f(x)=\frac{5}{x-6} \) \( \begin{array}{l}\{x \mid x>6\} \\ \{x \mid x \neq 6\} \\ \{x \mid x<6\}\end{array} \)

To find the domain of the function \( f(x)=\frac{5}{x-6} \), we need to identify any values of \( x \) that would make the denominator zero. In this case, \( x-6=0 \) leads to \( x=6 \). Thus, \( x \) cannot be 6, allowing all other real numbers for \( f(x) \). The domain is therefore \( \{x \mid x \neq 6\} \). When dealing with rational functions, it's crucial to remember that the denominator cannot equal zero; otherwise, the function is undefined. Therefore, look for any restrictions caused by denominators first, just like you did here! This approach saves you from headaches when graphing the function or evaluating its limits.