Question

find the domain of the function in interval notation: f(x) = \frac{1}{x + 16}

Explanation:

🆕 New Concept Discovered: Domain of Rational Functions
Finding where a fraction's denominator is zero

Step 1: Identify the restriction

For a rational function, the denominator cannot be equal to zero because division by zero is undefined.

Set the denominator not equal to zero:

$$ x + 16 eq 0 $$

Step 2: Solve for x

Subtract \( 16 \) from both sides to find the restricted value:

$$ x eq -16 $$

This means the domain includes all real numbers except \( -16 \).

Step 3: Write in interval notation

To exclude only the single value \( -16 \) from the entire real number line, we combine two open intervals using the union symbol (\(\cup\)):

$$ (-\infty, -16) \cup (-16, \infty) $$

Answer:

$$ (-\infty, -16) \cup (-16, \infty) $$