Find the Domain and Range f(x)=1/((x+4)^2)

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

Step 1

Set the denominator in $\frac{1}{{(x + 4)}^{2}}$ equal to $0$ to find where the expression is undefined.

${(x + 4)}^{2} = 0$

Step 2

Solve for $x$ .

Set the $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 3

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

Interval Notation:

$(- \infty, - 4) \cup (- 4, \infty)$

Set-Builder Notation:

${x | x \neq - 4}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(0, \infty)$

Set-Builder Notation:

${y | y > 0}$

Step 5

Determine the domain and range.

Domain: $(- \infty, - 4) \cup (- 4, \infty), {x | x \neq - 4}$

Range: $(0, \infty), {y | y > 0}$

Step 6