Calculus Examples

$f (x) = \frac{1}{\frac{1}{x}}$

Step 1

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

$x = 0$

Step 2

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

$\frac{1}{x} = 0$

Step 3

Solve for $x$ .

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Step 3.1

Set the numerator equal to zero.

$1 = 0$

Step 3.2

Since $1 \neq 0$ , there are no solutions.

No solution

Step 4

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$

Step 5