Precalculus Examples

$g (x) = - x^{2} - 1 - 2 x$ $f (x) = x + 5$ Find $(g - f) (x)$

Step 1

Evaluate $g - f$ .

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Step 1.1

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

$(- x^{2} - 1 - 2 x) - (x + 5)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$- x^{2} - 1 - 2 x - x - 1 \cdot 5$

Step 1.2.2

Multiply $- 1$ by $5$ .

$- x^{2} - 1 - 2 x - x - 5$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $5$ from $- 1$ .

$- x^{2} - 2 x - x - 6$

Step 1.3.2

Subtract $x$ from $- 2 x$ .

$- x^{2} - 3 x - 6$

Step 2

Evaluate $g - f$ at $x$ .

$- {(x)}^{2} - 3 x - 6$

Step 3

Simplify $- {(x)}^{2} - 3 x - 6$ .

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Step 3.1

Remove parentheses.

$- {(x)}^{2} - 3 x - 6$

Step 3.2

Remove parentheses.

$- x^{2} - 3 x - 6$