Questions: Determine the implied domain of the following function. Express your answer in interval notation. f(x) = 12 / (x - 12)

Solution Steps

To determine the implied domain of the function \( f(x) = \frac{12}{x-12} \), we need to identify the values of \( x \) for which the function is defined. The function is undefined when the denominator is zero. Therefore, we need to find the value of \( x \) that makes the denominator zero and exclude it from the domain.

To determine the implied domain of the function \( f(x) = \frac{12}{x-12} \), we first identify the denominator of the function, which is \( x - 12 \).

The function is undefined when the denominator is zero. Therefore, we solve the equation: \[ x - 12 = 0 \] Solving for \( x \), we get: \[ x = 12 \]

The domain of the function \( f(x) \) includes all real numbers except \( x = 12 \). In interval notation, this is expressed as: \[ (-\infty, 12) \cup (12, \infty) \]

Final Answer