Precalculus Examples

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

Step 1

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

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

Step 2

Solve for $x$ .

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Step 2.1

Subtract $1$ from $2$ .

$x^{2} + 1 \geq 0$

Step 2.2

Subtract $1$ from both sides of the inequality.

$x^{2} \geq - 1$

Step 2.3

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