Answer:
[tex]D_{f(x)} = (-\infty, \infty)[/tex]
Step-by-step explanation:
When we have a function in the following format:
[tex]f(x) = \sqrt[n]{g(x)}[/tex]
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:
[tex]f(x) = \sqrt[3]{10 - 11x}[/tex]
So [tex]g(x) = 10 - 11x[/tex]
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
[tex]D_{f(x)} = (-\infty, \infty)[/tex]
