Precalculus Examples

$G (x) = \frac{\sqrt{x - 3}}{x - 7}$

Step 1

Set the radicand in $\sqrt{x - 3}$ greater than or equal to $0$ to find where the expression is defined.

$x - 3 \geq 0$

Step 2

Add $3$ to both sides of the inequality.

$x \geq 3$

Step 3

Set the denominator in $\frac{\sqrt{x - 3}}{x - 7}$ equal to $0$ to find where the expression is undefined.

$x - 7 = 0$

Step 4

Add $7$ to both sides of the equation.

$x = 7$

Step 5

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

Interval Notation:

$[3, 7) \cup (7, \infty)$

Set-Builder Notation:

${x | x \geq 3, x \neq 7}$

Step 6