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.