\( 1 \leftarrow \quad \) 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.)

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:** \(\boxed{\,(-\infty,\ 11)\ \cup\ (11,\ 12)\ \cup\ (12,\ \infty)\,}\)