Examples

f (x) = \frac{1}{x}

$f (x) = \frac{1}{x}$ ,

g (x) = x^{2}

$g (x) = x^{2}$ ,

f (g (x))

$f (g (x))$

Step 1

Set up the composite result function.

f (g (x))

$f (g (x))$

Step 2

Evaluate

f (x^{2})

$f (x^{2})$ by substituting in the value of

g

$g$ into

f

$f$ .

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

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

Step 3

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 4

Solve for

x

$x$ .

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Step 4.1

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 4.2

Simplify

\pm \sqrt{0}

$\pm \sqrt{0}$ .

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Step 4.2.1

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

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

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

Step 4.2.2

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

x = \pm 0

$x = \pm 0$

Step 4.2.3

Plus or minus

0

$0$ is

0

$0$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

Step 5

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 6

Enter YOUR Problem