Precalculus Examples

$f (x) = \sqrt{{(x - 1)}^{2}}$

Step 1

Set the radicand in $\sqrt{{(x - 1)}^{2}}$ greater than or equal to $0$ to find where the expression is defined.

${(x - 1)}^{2} \geq 0$

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