Find the Domain and Range log base 1/2 of x

$\log_{\frac{1}{2}} (x)$

Set the argument in $\log_{\frac{1}{2}} (x)$ greater than $0$ to find where the expression is defined.

$x > 0$

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

Interval Notation:

$(0, \infty)$

Set-Builder Notation:

${x | x > 0}$

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

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Determine the domain and range.

Domain: $(0, \infty), {x | x > 0}$

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