Algebra Examples

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

Step 1

Evaluate $f - g$ .

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Step 1.1

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

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$3 x^{2} - 4 - x - 1 \cdot 2$

Step 1.2.2

Multiply $- 1$ by $2$ .

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

Step 1.3

Subtract $2$ from $- 4$ .

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

Step 2

Evaluate $f - g$ at $x$ .

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

Step 3

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

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Step 3.1

Remove parentheses.

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

Step 3.2

Multiply $- 1$ by $x$ .

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