Precalculus Examples

If $f (x) = 4 x^{2} - 3 x$ and $g (x) = 6 - 7 x$ ; find: $(f - g) (- 2)$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(4 x^{2} - 3 x) - (6 - 7 x)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$4 x^{2} - 3 x - 1 \cdot 6 - (- 7 x)$

Step 1.2.2

Multiply $- 1$ by $6$ .

$4 x^{2} - 3 x - 6 - (- 7 x)$

Step 1.2.3

Multiply $- 7$ by $- 1$ .

$4 x^{2} - 3 x - 6 + 7 x$

Step 1.3

Add $- 3 x$ and $7 x$ .

$4 x^{2} + 4 x - 6$

Step 2

Evaluate $f - g$ at $- 2$ .

$4 {(- 2)}^{2} + 4 (- 2) - 6$

Step 3

Simplify $4 {(- 2)}^{2} + 4 (- 2) - 6$ .

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Step 3.1

Remove parentheses.

$4 {(- 2)}^{2} + 4 (- 2) - 6$

Step 3.2

Simplify each term.

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Step 3.2.1

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

$4 \cdot 4 + 4 (- 2) - 6$

Step 3.2.2

Multiply $4$ by $4$ .

$16 + 4 (- 2) - 6$

Step 3.2.3

Multiply $4$ by $- 2$ .

$16 - 8 - 6$

Step 3.3

Simplify by subtracting numbers.

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Step 3.3.1

Subtract $8$ from $16$ .

$8 - 6$

Step 3.3.2

Subtract $6$ from $8$ .

$2$