Precalculus Examples

Let $f (x) = 3 x + 2$ and $g (x) = 6 x - 7$ Find $f (x) - g (x)$

Step 1

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

$(3 x + 2) - (6 x - 7)$

Step 2

Simplify $(3 x + 2) - (6 x - 7)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 x + 2 - (6 x) - - 7$

Step 2.1.2

Multiply $6$ by $- 1$ .

$3 x + 2 - 6 x - - 7$

Step 2.1.3

Multiply $- 1$ by $- 7$ .

$3 x + 2 - 6 x + 7$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $6 x$ from $3 x$ .

$- 3 x + 2 + 7$

Step 2.2.2

Add $2$ and $7$ .

$- 3 x + 9$