Examples

f (x) = x^{2} - 1

$f (x) = x^{2} - 1$ ,

g (x) = 2 x

$g (x) = 2 x$

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in

f (x) \cdot (g (x))

$f (x) \cdot (g (x))$ .

(x^{2} - 1) \cdot (2 x)

$(x^{2} - 1) \cdot (2 x)$

Step 1.2

Simplify.

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Step 1.2.1

Apply the distributive property.

x^{2} (2 x) - 1 (2 x)

$x^{2} (2 x) - 1 (2 x)$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

2 x^{2} x - 1 (2 x)

$2 x^{2} x - 1 (2 x)$

Step 1.2.2.2

Multiply

2

$2$ by

- 1

$- 1$ .

2 x^{2} x - 2 x

$2 x^{2} x - 2 x$

2 x^{2} x - 2 x

$2 x^{2} x - 2 x$

Step 1.2.3

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 1.2.3.1

Move

x

$x$ .

2 (x \cdot x^{2}) - 2 x

$2 (x \cdot x^{2}) - 2 x$

Step 1.2.3.2

Multiply

x

$x$ by

x^{2}

$x^{2}$ .

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Step 1.2.3.2.1

Raise

x

$x$ to the power of

1

$1$ .

2 (x^{1} x^{2}) - 2 x

$2 (x^{1} x^{2}) - 2 x$

Step 1.2.3.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

2 x^{1 + 2} - 2 x

$2 x^{1 + 2} - 2 x$

2 x^{1 + 2} - 2 x

$2 x^{1 + 2} - 2 x$

Step 1.2.3.3

Add

1

$1$ and

2

$2$ .

2 x^{3} - 2 x

$2 x^{3} - 2 x$

2 x^{3} - 2 x

$2 x^{3} - 2 x$

2 x^{3} - 2 x

$2 x^{3} - 2 x$

2 x^{3} - 2 x

$2 x^{3} - 2 x$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(- \infty, \infty)

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

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