Ensembles finis Exemples

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

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

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

Step 1.2

Simplify.

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Step 1.2.1

Apply the distributive property.

$x^{2} x + 2 x \cdot x + 1 x$

Step 1.2.2

Simplify.

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Step 1.2.2.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.2.2.1.1

Multiply $x^{2}$ by $x$ .

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Step 1.2.2.1.1.1

Raise $x$ to the power of $1$ .

$x^{2} x^{1} + 2 x \cdot x + 1 x$

Step 1.2.2.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1} + 2 x \cdot x + 1 x$

Step 1.2.2.1.2

Add $2$ and $1$ .

$x^{3} + 2 x \cdot x + 1 x$

Step 1.2.2.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.2.2.1

Move $x$ .

$x^{3} + 2 (x \cdot x) + 1 x$

Step 1.2.2.2.2

Multiply $x$ by $x$ .

$x^{3} + 2 x^{2} + 1 x$

Step 1.2.2.3

Multiply $x$ by $1$ .

$x^{3} + 2 x^{2} + x$

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:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

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