Question

at what points is the function continuous?
y=(12 - 11x)^{\frac{1}{9}}
the function is continuous on . (type your answer in interval notation.)

Explanation:

Step1: Recall continuity condition

A function of the form $y = u^{\frac{1}{n}}$ is continuous when $u\geq0$ for even $n$ and for all real - valued $u$ when $n$ is odd. Here $n = 9$ (odd).

Step2: Determine domain

Since $n = 9$ (odd), the function $y=(12 - 11x)^{\frac{1}{9}}$ is defined for all real values of $x$ because we can take the ninth - root of any real number.

Answer:

$(-\infty,\infty)$