Find the Domain and Range f(x) = log base 0.5 of x+3

$f (x) = \log_{0.5} (x + 3)$

Step 1

Set the argument in $\log_{0.5} (x + 3)$ greater than $0$ to find where the expression is defined.

$x + 3 > 0$

Step 2

Subtract $3$ from both sides of the inequality.

$x > - 3$

Step 3

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

Interval Notation:

$(- 3, \infty)$

Set-Builder Notation:

${x | x > - 3}$

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: $(- 3, \infty), {x | x > - 3}$

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

Step 6