Questions: Determine the implied domain of the following function. Express your answer in interval notation. f(x) = 9 / (x - 8)

Solution Steps

To determine the implied domain of the function \( f(x) = \frac{9}{x-8} \), 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 values of \( x \) that do not make the denominator zero and express the domain in interval notation.

We are given the function \( f(x) = \frac{9}{x - 8} \). To determine its implied domain, we need to analyze the denominator.

The function is undefined when the denominator is equal to zero. We set the denominator \( x - 8 = 0 \) and solve for \( x \): \[ x = 8 \]

Since the function is undefined at \( x = 8 \), the domain consists of all real numbers except \( 8 \). In interval notation, this is expressed as: \[ (-\infty, 8) \cup (8, \infty) \]

Final Answer