Question: Find the domain of the function. (Enter your answer using interval notation.) \[ f(x) = \frac{x…

Find the domain of the function. (Enter your answer using interval notation.)

\[ f(x) = \frac{x + 4}{x^2 - 4} \]

Solution

To find the domain of the function \( f(x) = \frac{x + 4}{x^2 - 4} \): The denominator cannot be zero, so set the denominator not equal to zero: \[ x^2 - 4 \neq 0 \] Solve for \( x \): \[ x^2 \neq 4 \] \[ x \neq \pm 2 \] Therefore, the domain is all real numbers except \( x = -2 \) and \( x = 2 \), so in interval notation: \[ (-\infty, -2) \cup (-2, 2) \cup (2, \infty) \]