Precalculus Examples

$g (x) = 4 x + 3$ $f (x) = x^{2} - 1$ Find $(g - f) (8)$

Step 1

Evaluate $g - f$ .

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Step 1.1

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

$(4 x + 3) - (x^{2} - 1)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$4 x + 3 - x^{2} - - 1$

Step 1.2.2

Multiply $- 1$ by $- 1$ .

$4 x + 3 - x^{2} + 1$

Step 1.3

Simplify the expression.

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Step 1.3.1

Add $3$ and $1$ .

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

Step 1.3.2

Reorder $4 x$ and $- x^{2}$ .

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

Step 2

Evaluate $g - f$ at $8$ .

$- {(8)}^{2} + 4 (8) + 4$

Step 3

Simplify $- {(8)}^{2} + 4 (8) + 4$ .

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Step 3.1

Remove parentheses.

$- {(8)}^{2} + 4 (8) + 4$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $8$ to the power of $2$ .

$- 1 \cdot 64 + 4 (8) + 4$

Step 3.2.2

Multiply $- 1$ by $64$ .

$- 64 + 4 (8) + 4$

Step 3.2.3

Multiply $4$ by $8$ .

$- 64 + 32 + 4$

Step 3.3

Simplify by adding numbers.

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Step 3.3.1

Add $- 64$ and $32$ .

$- 32 + 4$

Step 3.3.2

Add $- 32$ and $4$ .

$- 28$