Precalculus Examples

If $f (x) = x^{2} + 5 x$ and $g (x) = 7 - x$ ; 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.

$x^{2} + 5 x + 7 - x$

Step 1.2

Remove parentheses.

$x^{2} + 5 x + 7 - x$

Step 1.3

Subtract $x$ from $5 x$ .

$x^{2} + 4 x + 7$

Step 2

Evaluate $f + g$ at $2$ .

${(2)}^{2} + 4 (2) + 7$

Step 3

Simplify ${(2)}^{2} + 4 (2) + 7$ .

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Step 3.1

Remove parentheses.

${(2)}^{2} + 4 (2) + 7$

Step 3.2

Simplify each term.

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Step 3.2.1

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

$4 + 4 (2) + 7$

Step 3.2.2

Multiply $4$ by $2$ .

$4 + 8 + 7$

Step 3.3

Simplify by adding numbers.

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Step 3.3.1

Add $4$ and $8$ .

$12 + 7$

Step 3.3.2

Add $12$ and $7$ .

$19$