Precalculus Examples

If $f (x) = 4 x^{2} - 3 x$ and $g (x) = 6 - 7 x$ ; find: $(f + g) (5)$

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

Remove parentheses.

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

Step 1.3

Subtract $7 x$ from $- 3 x$ .

$4 x^{2} - 10 x + 6$

Step 2

Evaluate $f + g$ at $5$ .

$4 {(5)}^{2} - 10 \cdot 5 + 6$

Step 3

Simplify $4 {(5)}^{2} - 10 \cdot 5 + 6$ .

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Step 3.1

Remove parentheses.

$4 {(5)}^{2} - 10 \cdot 5 + 6$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $5$ to the power of $2$ .

$4 \cdot 25 - 10 \cdot 5 + 6$

Step 3.2.2

Multiply $4$ by $25$ .

$100 - 10 \cdot 5 + 6$

Step 3.2.3

Multiply $- 10$ by $5$ .

$100 - 50 + 6$

Step 3.3

Simplify by adding and subtracting.

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Step 3.3.1

Subtract $50$ from $100$ .

$50 + 6$

Step 3.3.2

Add $50$ and $6$ .

$56$