Precalculus Examples

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

Step 1

Set the radicand in $\sqrt{\frac{2}{x - 1}}$ greater than or equal to $0$ to find where the expression is defined.

$\frac{2}{x - 1} \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Find all the values where the expression switches from negative to positive by setting each factor equal to $0$ and solving.

$x - 1 = 0$

Step 2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.3

Find the domain of $\frac{2}{x - 1}$ .

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Step 2.3.1

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

$x - 1 = 0$

Step 2.3.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.3.3

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

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

Step 2.4

The solution consists of all of the true intervals.

$x > 1$

Step 3

Set the denominator in $\frac{2}{x - 1}$ 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:

$(1, \infty)$

Set-Builder Notation:

${x | x > 1}$

Step 6