Question

at what points is the given function f(x) continuous?
f(x)=\frac{11}{x - 10}-7x
describe the set of x - values where the function is continuous, using interval notation.

Explanation:

Step1: Identify the discontinuity point

A rational - function has a discontinuity where the denominator is zero. Set $x - 10=0$. Solving for $x$ gives $x = 10$.

Step2: Determine the intervals of continuity

The function $f(x)=\frac{11}{x - 10}-7x$ is a rational - function combined with a linear function. It is continuous everywhere except at $x = 10$.
The intervals of continuity are $(-\infty,10)$ and $(10,\infty)$.

Answer:

$(-\infty,10)\cup(10,\infty)$