Examples

f (x) = 2 x + 2

$f (x) = 2 x + 2$ ,

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))

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

(2 x + 2) \cdot (2 x)

$(2 x + 2) \cdot (2 x)$

Step 1.2

Simplify.

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Step 1.2.1

Simplify by multiplying through.

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Step 1.2.1.1

Apply the distributive property.

2 x (2 x) + 2 (2 x)

$2 x (2 x) + 2 (2 x)$

Step 1.2.1.2

Simplify the expression.

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Step 1.2.1.2.1

Rewrite using the commutative property of multiplication.

2 \cdot 2 x \cdot x + 2 (2 x)

$2 \cdot 2 x \cdot x + 2 (2 x)$

Step 1.2.1.2.2

Multiply

2

$2$ by

2

$2$ .

2 \cdot 2 x \cdot x + 4 x

$2 \cdot 2 x \cdot x + 4 x$

2 \cdot 2 x \cdot x + 4 x

$2 \cdot 2 x \cdot x + 4 x$

2 \cdot 2 x \cdot x + 4 x

$2 \cdot 2 x \cdot x + 4 x$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 1.2.2.1.1

Move

x

$x$ .

2 \cdot 2 (x \cdot x) + 4 x

$2 \cdot 2 (x \cdot x) + 4 x$

Step 1.2.2.1.2

Multiply

x

$x$ by

x

$x$ .

2 \cdot 2 x^{2} + 4 x

$2 \cdot 2 x^{2} + 4 x$

2 \cdot 2 x^{2} + 4 x

$2 \cdot 2 x^{2} + 4 x$

Step 1.2.2.2

Multiply

2

$2$ by

2

$2$ .

4 x^{2} + 4 x

$4 x^{2} + 4 x$

4 x^{2} + 4 x

$4 x^{2} + 4 x$

4 x^{2} + 4 x

$4 x^{2} + 4 x$

4 x^{2} + 4 x

$4 x^{2} + 4 x$

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}

${x | x \in ℝ}$

Step 3

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