Precalculus Examples

$f (x) = \frac{1}{| x | + 3}$

Step 1

Set the denominator in $\frac{1}{| x | + 3}$ equal to $0$ to find where the expression is undefined.

$| x | + 3 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $3$ from both sides of the equation.

$| x | = - 3$

Step 2.2

There is no value of $x$ that makes the equation be true since an absolute value can never be negative.

No solution

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4