Precalculus Examples

$f (x) = - x^{2} + 6 x - 1$ and $g (x) = 3 x^{2} - 4 x - 1$ ; find $(f + g) (x)$

Step 1

Evaluate $f + g$ .

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Step 1.1

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

$- x^{2} + 6 x - 1 + 3 x^{2} - 4 x - 1$

Step 1.2

Remove parentheses.

$- x^{2} + 6 x - 1 + 3 x^{2} - 4 x - 1$

Step 1.3

Add $- x^{2}$ and $3 x^{2}$ .

$2 x^{2} + 6 x - 1 - 4 x - 1$

Step 1.4

Subtract $4 x$ from $6 x$ .

$2 x^{2} + 2 x - 1 - 1$

Step 1.5

Subtract $1$ from $- 1$ .

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

Step 2

Evaluate $f + g$ at $x$ .

$2 {(x)}^{2} + 2 (x) - 2$

Step 3

Simplify $2 {(x)}^{2} + 2 (x) - 2$ .

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Step 3.1

Remove parentheses.

$2 {(x)}^{2} + 2 (x) - 2$

Step 3.2

Multiply $2$ by $x$ .

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