Find the domain of the function using interval notation. f(x)=\sqrt[3]{10-11x}

Question

Find the domain of the function using interval notation.

`f(x)=\sqrt[3]{10-11x}`

Answer 1

`D_(f(x)) = (-\infty, \infty)`

Explanation:

When we have a function in the following format:

`f(x) = \sqrt[n]{g(x)}`

And n is odd(3,5,...)

There are no impediments for the root,

So the domain of f(x) will be the domain of g(x)

In this problem, we have that:

`f(x) = \sqrt[3]{10 - 11x}`

So
`g(x) = 10 - 11x`

This is a subtraction of integers numbers, which has no impediment(denominator, for example).

So the domain are all the real numbers.

In interval notation

`D_(f(x)) = (-\infty, \infty)`