Precalculus Examples

$g (t) = 2 t + 5$ $f (t) = - t^{2} + 5$ Find $(g + f) (t)$

Step 1

Evaluate $g + f$ .

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Step 1.1

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

$2 t + 5 - t^{2} + 5$

Step 1.2

Remove parentheses.

$2 t + 5 - t^{2} + 5$

Step 1.3

Add $5$ and $5$ .

$2 t - t^{2} + 10$

Step 1.4

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

$- t^{2} + 2 t + 10$

Step 2

Evaluate $g + f$ at $t$ .

$- {(t)}^{2} + 2 (t) + 10$

Step 3

Simplify $- {(t)}^{2} + 2 (t) + 10$ .

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Step 3.1

Remove parentheses.

$- {(t)}^{2} + 2 (t) + 10$

Step 3.2

Multiply $2$ by $t$ .

$- t^{2} + 2 t + 10$