Find the Domain and Range y=cot(-x)

$y = \cot (- x)$

Step 1

Set the argument in $\cot (- x)$ equal to $π n$ to find where the expression is undefined.

$- x = π n$ , for any integer $n$

Step 2

Divide each term in $- x = π n$ by $- 1$ and simplify.

Divide each term in $- x = π n$ by $- 1$ .

$\frac{- x}{- 1} = \frac{π n}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{π n}{- 1}$

Divide $x$ by $1$ .

$x = \frac{π n}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{π n}{- 1}$ .

$x = - 1 \cdot (π n)$

Rewrite $- 1 \cdot (π n)$ as $- (π n)$ .

$x = - π n$

Step 3

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

Set-Builder Notation:

${x | x \neq - π n}$ , for any integer $n$

Step 4

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

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: ${x | x \neq - π n}$ , for any integer $n$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6