Precalculus Examples

$f (x) = \frac{\sqrt{x - 1}}{x - 4}$

Step 1

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

$x - 1 \geq 0$

Step 2

Add $1$ to both sides of the inequality.

$x \geq 1$

Step 3

Set the denominator in $\frac{\sqrt{x - 1}}{x - 4}$ equal to $0$ to find where the expression is undefined.

$x - 4 = 0$

Step 4

Add $4$ to both sides of the equation.

$x = 4$

Step 5

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

Interval Notation:

$[1, 4) \cup (4, \infty)$

Set-Builder Notation:

${x | x \geq 1, x \neq 4}$

Step 6