Precalculus Examples

$\log_{2} (x^{2} + 4)$

Set the argument in $\log_{2} (x^{2} + 4)$ greater than $0$ to find where the expression is defined.

$x^{2} + 4 > 0$

Solve for $x$ .

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Subtract $4$ from both sides of the inequality.

$x^{2} > - 4$

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

All real numbers

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:

${x | x \in ℝ}$