Precalculus Examples

$\sqrt{x^{2} + 3}$

Step 1

Set the radicand in $\sqrt{x^{2} + 3}$ greater than or equal to $0$ to find where the expression is defined.

$x^{2} + 3 \geq 0$

Step 2

Solve for $x$ .

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Subtract $3$ from both sides of the inequality.

$x^{2} \geq - 3$

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

All real numbers

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4