Precalculus Examples

$f (x) = 2 x + 1$ and $g (x) = x^{2} - 7$ ; find $(f - g) (x)$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$2 x + 1 - x^{2} - - 7$

Step 1.2.2

Multiply $- 1$ by $- 7$ .

$2 x + 1 - x^{2} + 7$

Step 1.3

Simplify the expression.

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Step 1.3.1

Add $1$ and $7$ .

$2 x - x^{2} + 8$

Step 1.3.2

Reorder $2 x$ and $- x^{2}$ .

$- x^{2} + 2 x + 8$

Step 2

Evaluate $f - g$ at $x$ .

$- {(x)}^{2} + 2 (x) + 8$

Step 3

Simplify $- {(x)}^{2} + 2 (x) + 8$ .

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Step 3.1

Remove parentheses.

$- {(x)}^{2} + 2 (x) + 8$

Step 3.2

Multiply $2$ by $x$ .

$- x^{2} + 2 x + 8$