$$ 1 \leftarrow \quad $$ Find the domain of the function. $$ f(x)=\frac{5}{x-11}+\frac{1}{x-12} $$ The domain of $$ f(x) $$ is $$ \square $$. (Type your answer in interval notation.)

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To find the **domain** of the function $$ f(x) = \frac{5}{x - 11} + \frac{1}{x - 12} $$, we need to determine all real numbers $$ x $$ for which the function is defined.

The function involves two denominators: $$ x - 11 $$ and $$ x - 12 $$. These denominators cannot be zero because division by zero is undefined. Therefore, we must exclude the values of $$ x $$ that make either denominator zero.

1. **First denominator**: $$ x - 11 \neq 0 $$  
   $$ x \neq 11 $$

2. **Second denominator**: $$ x - 12 \neq 0 $$  
   $$ x \neq 12 $$

Thus, the function $$ f(x) $$ is defined for all real numbers except $$ x = 11 $$ and $$ x = 12 $$.

**Domain in Interval Notation:**
$$ (-\infty, 11) \cup (11, 12) \cup (12, \infty) $$

**Answer:**  
$$\boxed{\,(-\infty,\ 11)\ \cup\ (11,\ 12)\ \cup\ (12,\ \infty)\,}$$
The domain of $$ f(x) $$ is all real numbers except $$ x = 11 $$ and $$ x = 12 $$. In interval notation, this is $$ (-\infty, 11) \cup (11, 12) \cup (12, \infty) $$.

\( 1 \leftarrow \quad \) Find the domain of the function. \( f(x)=\frac{5}{x-11}+\frac{1}{x-12} \) The domain of \( f(x) \) is \( \square \). (Type your answer in interval notation.)

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