Calculus Examples

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

Step 1

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

${(x + 1)}^{2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 2.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 3

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

Interval Notation:

$(- \infty, - 1) \cup (- 1, \infty)$

Set-Builder Notation:

${x | x \neq - 1}$

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

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

Step 6