To solve the problem of finding [tex]\((f + g)(x)\)[/tex] given the functions [tex]\( f(x) = 5^x + 2x \)[/tex] and [tex]\( g(x) = 3x - 6 \)[/tex], let's follow a step-by-step procedure:
1. Identify the Functions:
- [tex]\( f(x) = 5^x + 2x \)[/tex]
- [tex]\( g(x) = 3x - 6 \)[/tex]
2. Definition of the Combined Function [tex]\((f + g)(x)\)[/tex]:
[tex]\[
(f + g)(x) = f(x) + g(x)
\][/tex]
3. Substitute [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into the Combined Function:
[tex]\[
(f + g)(x) = (5^x + 2x) + (3x - 6)
\][/tex]
4. Combine Like Terms:
- Combine the [tex]\( x \)[/tex]-terms: [tex]\( 2x \)[/tex] from [tex]\( f(x) \)[/tex] and [tex]\( 3x \)[/tex] from [tex]\( g(x) \)[/tex]:
[tex]\[
2x + 3x = 5x
\][/tex]
- Combine the constant term from [tex]\( g(x) \)[/tex] with the terms involving [tex]\( 5^x \)[/tex]:
[tex]\[
5^x + 5x - 6
\][/tex]
5. Final Expression:
[tex]\[
(f + g)(x) = 5^x + 5x - 6
\][/tex]
So, the combined function [tex]\((f + g)(x)\)[/tex] simplifies to:
[tex]\[
5^x + 5x - 6
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{5^x + 5x - 6}
\][/tex]
