Precalculus Examples

$f (x) = 4 x - 3$ $g (x) = x^{3} + 2 x$ Find $(f - g) (4)$

Step 1

Evaluate $f - g$ .

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Step 1.1

Replace the function designators in $f - g$ with the actual functions.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$4 x - 3 - x^{3} - (2 x)$

Step 1.2.2

Multiply $2$ by $- 1$ .

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

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $2 x$ from $4 x$ .

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

Step 1.3.2

Simplify the expression.

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Step 1.3.2.1

Move $- 3$ .

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

Step 1.3.2.2

Reorder $2 x$ and $- x^{3}$ .

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

Step 2

Evaluate $f - g$ at $4$ .

$- {(4)}^{3} + 2 (4) - 3$

Step 3

Simplify $- {(4)}^{3} + 2 (4) - 3$ .

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Step 3.1

Remove parentheses.

$- {(4)}^{3} + 2 (4) - 3$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $4$ to the power of $3$ .

$- 1 \cdot 64 + 2 (4) - 3$

Step 3.2.2

Multiply $- 1$ by $64$ .

$- 64 + 2 (4) - 3$

Step 3.2.3

Multiply $2$ by $4$ .

$- 64 + 8 - 3$

Step 3.3

Simplify by adding and subtracting.

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Step 3.3.1

Add $- 64$ and $8$ .

$- 56 - 3$

Step 3.3.2

Subtract $3$ from $- 56$ .

$- 59$