Precalculus Examples

$x^{2} - \sqrt{1 + x^{2}} = \frac{2}{\sqrt[3]{x^{2} - 1}}$

Step 1

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

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

Step 2

Solve for $x$ .

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Step 2.1

Subtract $1$ from both sides of the inequality.

$x^{2} \geq - 1$

Step 2.2

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