Algebra Examples

$f^{- 1}$

Step 1

Set the base in $f^{- 1}$ equal to $0$ to find where the expression is undefined.

$f = 0$

Step 2

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

Interval Notation:

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

Set-Builder Notation:

${f | f \neq 0}$

Step 3

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

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

Set-Builder Notation:

${y | y \neq 0}$

Step 4

Determine the domain and range.

Domain: $(- \infty, 0) \cup (0, \infty), {f | f \neq 0}$

Range: $(- \infty, 0) \cup (0, \infty), {y | y \neq 0}$

Step 5