Precalculus Examples

Given that $f (x) = x^{2} - 5 x - 14$ and $g (x) = x - 7$ ; find $(f + g) (x)$ and express the result in standard form.

Step 1

Evaluate $f + g$ .

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Step 1.1

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

$x^{2} - 5 x - 14 + x - 7$

Step 1.2

Remove parentheses.

$x^{2} - 5 x - 14 + x - 7$

Step 1.3

Add $- 5 x$ and $x$ .

$x^{2} - 4 x - 14 - 7$

Step 1.4

Subtract $7$ from $- 14$ .

$x^{2} - 4 x - 21$

Step 2

Evaluate $f + g$ at $x$ .

${(x)}^{2} - 4 x - 21$

Step 3

Simplify ${(x)}^{2} - 4 x - 21$ .

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Step 3.1

Remove parentheses.

${(x)}^{2} - 4 x - 21$

Step 3.2

Remove parentheses.

$x^{2} - 4 x - 21$