Why is $|x| \neq x$? I was just thinking about the absolute value function. Why does the following equality not hold?
$$|x| = \sqrt{x^2} = (x^{2})^{1/2} = x^1 = x$$
After all, there are clearly some values of $|x|$ that are not equal to $x$. Is this a domain/range issue?

It should be:
$$\sqrt{x^2} = (|x|^{2})^{1/2} = |x|^1 = |x|$$
