Question

What is the domain of the function y=^3sqrt (x-1)

Answer 1

If the equation is
`y = \sqrt[3]{x-1}` then the domain is the set of all real numbers.

We can replace x with any real number and compute to get some real number output for y. There are no division by zero restrictions to worry about, or issues with taking a square root of a negative number (since this isn't really a square root function).

The cube root of a negative number is negative. For example,
`\sqrt[3]{-64} = -4` because (-4)^3 = (-4)*(-4)*(-4) = -64.

In interval notation, the domain would be written as
`(-\infty, \infty)` to indicate the entire real number line.