Question

What is the domain of the function

Answer 1

Answer:
`-\infty < \text{x} < \infty` (Choice A)

Reason:

We can replace x with any real number to generate some output for y. Negative x values are allowed in the domain. We don't have to worry about things like taking a square root of a negative number.

For instance if x = -216 then

`y = \sqrt[3]{\text{x}}\\\\y = \sqrt[3]{-216}\\\\y = \sqrt[3]{(-6)^3}\\\\y = -6`

This is why the domain is the set of all real numbers. As an inequality, we would write
`-\infty < \text{x} < \infty`

This could be condensed down to the interval notation
`(-\infty, \infty)`