Given \( f(x)=\frac{x^{2}+x-30}{x-5} \), Part 1 of 5 (a) Write the domain of \( f \) in interval notation. The domain of the function in interval notation is

To determine the domain of the function \( f(x) = \frac{x^{2} + x - 30}{x - 5} \), we need to identify any values of \( x \) that would make the denominator equal to zero, as these values are not included in the domain. 1. **Identify the denominator**: The denominator is \( x - 5 \). 2. **Set the denominator to zero**: \[ x - 5 = 0 \] Solving this gives: \[ x = 5 \] 3. **Determine the domain**: The function is defined for all real numbers except \( x = 5 \). Therefore, the domain in interval notation excludes this point. The domain of the function in interval notation is: \[ (-\infty, 5) \cup (5, \infty) \]