Algebra Examples

y = \frac{1}{x^{2}}

$y = \frac{1}{x^{2}}$

Step 1

Set the denominator in

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ equal to

0

$0$ to find where the expression is undefined.

x^{2} = 0

$x^{2} = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x = \pm \sqrt{0}

$x = \pm \sqrt{0}$

Step 2.2

Simplify

\pm \sqrt{0}

$\pm \sqrt{0}$ .

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Step 2.2.1

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

x = \pm \sqrt{0^{2}}

$x = \pm \sqrt{0^{2}}$

Step 2.2.2

Pull terms out from under the radical, assuming positive real numbers.

x = \pm 0

$x = \pm 0$

Step 2.2.3

Plus or minus

0

$0$ is

0

$0$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

Step 3

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

(- \infty, 0) \cup (0, \infty)

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

{x | x \neq 0}

${x | x \neq 0}$

Step 4

The range is the set of all valid

y

$y$ values. Use the graph to find the range.

Interval Notation:

(0, \infty)

$(0, \infty)$

Set-Builder Notation:

{y | y > 0}

${y | y > 0}$

Step 5

Determine the domain and range.

Domain:

(- \infty, 0) \cup (0, \infty), {x | x \neq 0}

$(- \infty, 0) \cup (0, \infty), {x | x \neq 0}$

Range:

(0, \infty), {y | y > 0}

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

Step 6

y = \frac{1}{x^{2}}

$y = \frac{1}{x^{2}}$

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