Precalculus Examples

$\sqrt{x^{2}} - 4$

Step 1

Set the radicand in $\sqrt{x^{2}}$ greater than or equal to $0$ to find where the expression is defined.

$x^{2} \geq 0$

Step 2

Since the left side has an even power, it is always positive for all real numbers.

All real numbers

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4