Questions: At what points is the given function (f(x)) continuous? (f(x)=frac8x-9-9 x)

Solution Steps

To determine the points at which the function \( f(x) = \frac{8}{x-9} - 9x \) is continuous, we need to identify any points where the function is undefined. The function is undefined where the denominator is zero. Therefore, we need to find the values of \( x \) that make the denominator zero and exclude those from the domain of the function.

We are given the function: \[ f(x) = \frac{8}{x-9} - 9x \]

To determine where the function is continuous, we need to find where it is undefined. The function \( f(x) \) is undefined where the denominator is zero. Therefore, we solve: \[ x - 9 = 0 \] \[ x = 9 \]

The function \( f(x) \) is continuous for all \( x \) except where it is undefined. Thus, \( f(x) \) is continuous for: \[ x \in \mathbb{R} \setminus \{9\} \]

Final Answer