Precalculus Examples

$f (x) = 3^{x} + 10$ and $g (x) = 2 x - 4$ ; 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.

$3^{x} + 10 + 2 x - 4$

Step 1.2

Remove parentheses.

$3^{x} + 10 + 2 x - 4$

Step 1.3

Subtract $4$ from $10$ .

$3^{x} + 2 x + 6$

Step 1.4

Reorder $3^{x}$ and $2 x$ .

$2 x + 3^{x} + 6$

Step 2

Evaluate $f + g$ at $x$ .

$2 (x) + 3^{x} + 6$

Step 3

Simplify $2 (x) + 3^{x} + 6$ .

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Step 3.1

Remove parentheses.

$2 (x) + 3^{x} + 6$

Step 3.2

Multiply $2$ by $x$ .

$2 x + 3^{x} + 6$