Finite Math Examples

$c (x) = 9500 + 23 x$ , $r (x) = 43 x$

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in $c (x) \cdot (r (x))$ .

$(9500 + 23 x) \cdot (43 x)$

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.

$9500 (43 x) + 23 x (43 x)$

Step 1.2.1.2

Simplify the expression.

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Step 1.2.1.2.1

Multiply $43$ by $9500$ .

$408500 x + 23 x (43 x)$

Step 1.2.1.2.2

Rewrite using the commutative property of multiplication.

$408500 x + 23 \cdot 43 x \cdot x$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

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

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Step 1.2.2.1.1

Move $x$ .

$408500 x + 23 \cdot 43 (x \cdot x)$

Step 1.2.2.1.2

Multiply $x$ by $x$ .

$408500 x + 23 \cdot 43 x^{2}$

Step 1.2.2.2

Multiply $23$ by $43$ .

$408500 x + 989 x^{2}$

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