Precalculus Examples

$g (x) = 3 x + 3$ $f (x) = 2 x - 3$ Find $(g - f) (- 9)$

Step 1

Evaluate $g - f$ .

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Step 1.1

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

$(3 x + 3) - (2 x - 3)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$3 x + 3 - (2 x) - - 3$

Step 1.2.2

Multiply $2$ by $- 1$ .

$3 x + 3 - 2 x - - 3$

Step 1.2.3

Multiply $- 1$ by $- 3$ .

$3 x + 3 - 2 x + 3$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $2 x$ from $3 x$ .

$x + 3 + 3$

Step 1.3.2

Add $3$ and $3$ .

$x + 6$

Step 2

Evaluate $g - f$ at $- 9$ .

$(- 9) + 6$

Step 3

Simplify $(- 9) + 6$ .

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Step 3.1

Remove parentheses.

$(- 9) + 6$

Step 3.2

Add $- 9$ and $6$ .

$- 3$