Precalculus Examples

$g (a) = - 3 a - 3$ $f (a) = a^{2} + 5$ find $(g - f) (a)$

Step 1

Evaluate $g - f$ .

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Step 1.1

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

$(- 3 a - 3) - (a^{2} + 5)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$- 3 a - 3 - a^{2} - 1 \cdot 5$

Step 1.2.2

Multiply $- 1$ by $5$ .

$- 3 a - 3 - a^{2} - 5$

Step 1.3

Simplify the expression.

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Step 1.3.1

Subtract $5$ from $- 3$ .

$- 3 a - a^{2} - 8$

Step 1.3.2

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

$- a^{2} - 3 a - 8$

Step 2

Evaluate $g - f$ at $a$ .

$- {(a)}^{2} - 3 a - 8$

Step 3

Simplify $- {(a)}^{2} - 3 a - 8$ .

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Step 3.1

Remove parentheses.

$- {(a)}^{2} - 3 a - 8$

Step 3.2

Remove parentheses.

$- a^{2} - 3 a - 8$