Question

at what points is the given function f(x) continuous? f(x)=\frac{9}{x - 11}-2x. describe the set of x - values where the function is continuous, using interval notation. (use interval notation.)

Explanation:

Step1: Recall continuity condition

A rational - function $\frac{g(x)}{h(x)}$ is discontinuous where $h(x)=0$. For $f(x)=\frac{9}{x - 11}-2x$, the rational part $\frac{9}{x - 11}$ has a problem when $x-11 = 0$.

Step2: Solve for the discontinuity point

Set $x - 11=0$, then $x = 11$.

Step3: Determine the continuous intervals

The function $f(x)$ is continuous for all real - numbers except $x = 11$. In interval notation, the set of continuous $x$ values is $(-\infty,11)\cup(11,\infty)$.

Answer:

$(-\infty,11)\cup(11,\infty)$