Precalculus Examples

$f (x, y) = \sqrt{y - x - 2}$

Step 1

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

$y - x - 2 \geq 0$

Step 2

Move all terms not containing $y$ to the right side of the inequality.

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Step 2.1

Add $x$ to both sides of the inequality.

$y - 2 \geq x$

Step 2.2

Add $2$ to both sides of the inequality.

$y \geq x + 2$

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$