Precalculus Examples

Find $(f - g) (x)$ if $f (x) = 7 x^{2} + 2$ and $g (x) = 2 x^{2} + 9$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(7 x^{2} + 2) - (2 x^{2} + 9)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$7 x^{2} + 2 - (2 x^{2}) - 1 \cdot 9$

Step 1.2.2

Multiply $2$ by $- 1$ .

$7 x^{2} + 2 - 2 x^{2} - 1 \cdot 9$

Step 1.2.3

Multiply $- 1$ by $9$ .

$7 x^{2} + 2 - 2 x^{2} - 9$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $2 x^{2}$ from $7 x^{2}$ .

$5 x^{2} + 2 - 9$

Step 1.3.2

Subtract $9$ from $2$ .

$5 x^{2} - 7$

Step 2

Evaluate $f - g$ at $x$ .

$5 {(x)}^{2} - 7$

Step 3

Simplify $5 {(x)}^{2} - 7$ .

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Step 3.1

Remove parentheses.

$5 {(x)}^{2} - 7$

Step 3.2

Remove parentheses.

$5 x^{2} - 7$