Precalculus Examples

Given that $f (x) = x^{2} + 17 x + 70$ and $g (x) = x + 10$ ; 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.

$x^{2} + 17 x + 70 + x + 10$

Step 1.2

Remove parentheses.

$x^{2} + 17 x + 70 + x + 10$

Step 1.3

Add $17 x$ and $x$ .

$x^{2} + 18 x + 70 + 10$

Step 1.4

Add $70$ and $10$ .

$x^{2} + 18 x + 80$

Step 2

Evaluate $f + g$ at $x$ .

${(x)}^{2} + 18 (x) + 80$

Step 3

Simplify ${(x)}^{2} + 18 (x) + 80$ .

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Step 3.1

Remove parentheses.

${(x)}^{2} + 18 (x) + 80$

Step 3.2

Multiply $18$ by $x$ .

$x^{2} + 18 x + 80$