Find the Domain and Range y=x+1/x

$y = x + \frac{1}{x}$

Step 1

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

$x = 0$

Step 2

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 3

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

Interval Notation:

$(- \infty, - 2] \cup [2, \infty)$

Set-Builder Notation:

${y | y \leq - 2, y \geq 2}$

Step 4

Determine the domain and range.

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

Range: $(- \infty, - 2] \cup [2, \infty), {y | y \leq - 2, y \geq 2}$

Step 5