Find the Domain and Range f(x)=4 log base 1/3 of x+2

$f (x) = 4 \log_{\frac{1}{3}} (x + 2)$

Step 1

Set the argument in $\log_{\frac{1}{3}} (x + 2)$ greater than $0$ to find where the expression is defined.

$x + 2 > 0$

Step 2

Subtract $2$ from both sides of the inequality.

$x > - 2$

Step 3

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

Interval Notation:

$(- 2, \infty)$

Set-Builder Notation:

${x | x > - 2}$

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: $(- 2, \infty), {x | x > - 2}$

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

Step 6