Precalculus Examples

$h (x) = \sqrt{\frac{- 9}{x - 4}}$

Step 1

Set the radicand in $\sqrt{\frac{- 9}{x - 4}}$ greater than or equal to $0$ to find where the expression is defined.

$\frac{- 9}{x - 4} \geq 0$

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.

$- 9 = 0$

$x - 4 = 0$

Step 2.2

Since $- 9 \neq 0$ , there are no solutions.

No solution

Step 2.3

Add $4$ to both sides of the equation.

$x = 4$

Step 2.4

Find the domain of $\frac{- 9}{x - 4}$ .

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Step 2.4.1

Set the denominator in $\frac{- 9}{x - 4}$ equal to $0$ to find where the expression is undefined.

$x - 4 = 0$

Step 2.4.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.4.3

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

$(- \infty, 4) \cup (4, \infty)$

Step 2.5

The solution consists of all of the true intervals.

$x < 4$

Step 3

Set the denominator in $\frac{- 9}{x - 4}$ 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:

$(- \infty, 4)$

Set-Builder Notation:

${x | x < 4}$

Step 6