Precalculus Examples

$f (x) = 3 x + 5$ and $g (x) = - 2 x^{2} - 5 x + 3$ ; find $(f + g) (x)$

Step 1

Evaluate $f + g$ .

Tap for more steps...

Step 1.1

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

$3 x + 5 - 2 x^{2} - 5 x + 3$

Step 1.2

Remove parentheses.

$3 x + 5 - 2 x^{2} - 5 x + 3$

Step 1.3

Subtract $5 x$ from $3 x$ .

$- 2 x + 5 - 2 x^{2} + 3$

Step 1.4

Simplify the expression.

Tap for more steps...

Step 1.4.1

Add $5$ and $3$ .

$- 2 x - 2 x^{2} + 8$

Step 1.4.2

Reorder $- 2 x$ and $- 2 x^{2}$ .

$- 2 x^{2} - 2 x + 8$

Step 2

Evaluate $f + g$ at $x$ .

$- 2 {(x)}^{2} - 2 x + 8$

Step 3

Simplify $- 2 {(x)}^{2} - 2 x + 8$ .

Tap for more steps...

Step 3.1

Remove parentheses.

$- 2 {(x)}^{2} - 2 x + 8$

Step 3.2

Remove parentheses.

$- 2 x^{2} - 2 x + 8$