Question

use these functions to answer the question.
$f(x) = 2^{x}$
$g(x) = x^{2} + x + 3$
what is $(f + g)(x)$?
$2^{x} + x^{2} + x + 3$ $2^{x} + x + 3$
$2x^{2} + 2x + 6$ $2^{x^{2}+x + 3}$

Explanation:

Step1: Recall the definition of function addition

The sum of two functions \((f + g)(x)\) is defined as \(f(x) + g(x)\).

Step2: Substitute the given functions

We know that \(f(x)=2^{x}\) and \(g(x)=x^{2}+x + 3\). So, \((f + g)(x)=f(x)+g(x)=2^{x}+(x^{2}+x + 3)\).

Step3: Simplify the expression

Removing the parentheses, we get \(2^{x}+x^{2}+x + 3\).

Answer:

\(2^{x}+x^{2}+x + 3\) (the first option among the given choices)