Precalculus Examples

$\sqrt{y - x^{2}}$

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

Solve for $y$ .

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Step 2.1

Add $x^{2}$ to both sides of the inequality.

$y \geq x^{2}$

Step 2.2

Use each root to create test intervals.

$y < x^{2}$

$y > x^{2}$

Step 2.3

Compare the intervals to determine which ones satisfy the original inequality.

Step 2.4

Since there are no numbers that fall within the interval, this inequality has no solution.

No solution

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 4