Precalculus Examples

$f (x) = \frac{\sqrt{x - 2}}{x (x - 1)}$

Step 1

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

$x - 2 \geq 0$

Step 2

Add $2$ to both sides of the inequality.

$x \geq 2$

Step 3

Set the denominator in $\frac{\sqrt{x - 2}}{x (x - 1)}$ equal to $0$ to find where the expression is undefined.

$x (x - 1) = 0$

Step 4

Solve for $x$ .

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Step 4.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 1 = 0$

Step 4.2

Set $x$ equal to $0$ .

$x = 0$

Step 4.3

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 4.3.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 4.3.2

Add $1$ to both sides of the equation.

$x = 1$

Step 4.4

The final solution is all the values that make $x (x - 1) = 0$ true.

$x = 0, 1$

Step 5

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

Interval Notation:

$[2, \infty)$

Set-Builder Notation:

${x | x \geq 2}$

Step 6