Find the Domain and Range f(x) = log of x+6-4

$f (x) = \log (x + 6) - 4$

Step 1

Set the argument in $\log (x + 6)$ greater than $0$ to find where the expression is defined.

$x + 6 > 0$

Step 2

Subtract $6$ from both sides of the inequality.

$x > - 6$

Step 3

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

Interval Notation:

$(- 6, \infty)$

Set-Builder Notation:

${x | x > - 6}$

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: $(- 6, \infty), {x | x > - 6}$

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

Step 6