Question

Compare the domain:

Domain of y= square root of x is 0 < x < infinity Domain of the inverse y=x² is -infinity<x< infinity

What is the significant difference between the domains of y=square root of x and y= x²?

Answer 1

Solution:

Domain of $y=\sqrt{x}$ is $[0,\infty)$

Domain of $y=x^2$ is $(-\infty,\infty)$

The significant difference between their domains is that $y=\sqrt{x}$ cannot take negative values of $x$ because the square root of negative value does not exist in the real world.

This can be seen in the following graph: