Finite Math Examples

$f (x) = - x^{2}$ , $g (x) = 4 x - 1$

Step 1

Find the product of the functions.

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Step 1.1

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

$(- x^{2}) \cdot (4 x - 1)$

Step 1.2

Simplify.

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Step 1.2.1

Apply the distributive property.

$- x^{2} (4 x) - x^{2} \cdot - 1$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$- 1 \cdot 4 x^{2} x - x^{2} \cdot - 1$

Step 1.2.3

Multiply $- x^{2} \cdot - 1$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$- 1 \cdot 4 x^{2} x + 1 x^{2}$

Step 1.2.3.2

Multiply $x^{2}$ by $1$ .

$- 1 \cdot 4 x^{2} x + x^{2}$

Step 1.2.4

Simplify each term.

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Step 1.2.4.1

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

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Step 1.2.4.1.1

Move $x$ .

$- 1 \cdot 4 (x \cdot x^{2}) + x^{2}$

Step 1.2.4.1.2

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

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Step 1.2.4.1.2.1

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

$- 1 \cdot 4 (x^{1} x^{2}) + x^{2}$

Step 1.2.4.1.2.2

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

$- 1 \cdot 4 x^{1 + 2} + x^{2}$

Step 1.2.4.1.3

Add $1$ and $2$ .

$- 1 \cdot 4 x^{3} + x^{2}$

Step 1.2.4.2

Multiply $- 1$ by $4$ .

$- 4 x^{3} + x^{2}$

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