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

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

Step 1

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

$x + 1 > 0$

Step 2

Subtract $1$ from both sides of the inequality.

$x > - 1$

Step 3

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

Interval Notation:

$(- 1, \infty)$

Set-Builder Notation:

${x | x > - 1}$

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: $(- 1, \infty), {x | x > - 1}$

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

Step 6