Find the Domain and Range f(x)=- natural log of x+5

$f (x) = - \ln (x + 5)$

Set the argument in $\ln (x + 5)$ greater than $0$ to find where the expression is defined.

$x + 5 > 0$

Subtract $5$ from both sides of the inequality.

$x > - 5$

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

Interval Notation:

$(- 5, \infty)$

Set-Builder Notation:

${x | x > - 5}$

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: $(- 5, \infty), {x | x > - 5}$

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