To find [tex]\((f + g)(x)\)[/tex] when given the functions [tex]\(f(x) = 3^x + 10x\)[/tex] and [tex]\(g(x) = 5x - 3\)[/tex], we need to add these two functions together.
The combined function [tex]\((f + g)(x)\)[/tex] is given by [tex]\(f(x) + g(x)\)[/tex].
1. We start by writing down [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
f(x) = 3^x + 10x
\][/tex]
[tex]\[
g(x) = 5x - 3
\][/tex]
2. Next, we add [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f + g)(x) = f(x) + g(x)
\][/tex]
3. Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into this equation:
[tex]\[
(f + g)(x) = (3^x + 10x) + (5x - 3)
\][/tex]
4. Combine like terms:
[tex]\[
(f + g)(x) = 3^x + 10x + 5x - 3
\][/tex]
[tex]\[
(f + g)(x) = 3^x + (10x + 5x) - 3
\][/tex]
[tex]\[
(f + g)(x) = 3^x + 15x - 3
\][/tex]
Therefore, the combined function [tex]\((f + g)(x)\)[/tex] is:
[tex]\[
(f + g)(x) = 3^x + 15x - 3
\][/tex]
Thus, the correct answer is:
A. [tex]\(3^x + 15x - 3\)[/tex].
