Find the Domain and Range f(x)=-1/2* natural log of x+3

$f (x) = - \frac{1}{2} \cdot \ln (x + 3)$

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

$x + 3 > 0$

Subtract $3$ from both sides of the inequality.

$x > - 3$

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

Interval Notation:

$(- 3, \infty)$

Set-Builder Notation:

${x | x > - 3}$

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

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