Precalculus Examples

$f (x, y) = \frac{\sqrt{x + y + 1}}{x - 1}$

Step 1

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

$x + y + 1 \geq 0$

Step 2

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

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Step 2.1

Subtract $y$ from both sides of the inequality.

$x + 1 \geq - y$

Step 2.2

Subtract $1$ from both sides of the inequality.

$x \geq - y - 1$

Step 3

Set the denominator in $\frac{\sqrt{x + y + 1}}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Step 4

Add $1$ to both sides of the equation.

$x = 1$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 1) \cup (1, \infty)$

Set-Builder Notation:

${x | x \neq 1}$