To solve for [tex]\( (f+g)(x) \)[/tex], we need to add the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] together. Let's break this down step-by-step:
1. Understand the given functions:
- [tex]\( f(x) = 3^x + 10x \)[/tex]
- [tex]\( g(x) = 2x - 4 \)[/tex]
2. Add the functions together:
[tex]\[
f(x) + g(x) = (3^x + 10x) + (2x - 4)
\][/tex]
3. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( 10x + 2x = 12x \)[/tex]
- The constant term is [tex]\(-4\)[/tex]
- [tex]\( 3^x \)[/tex] remains as it is
4. Write the resulting expression:
[tex]\[
(f+g)(x) = 3^x + 12x - 4
\][/tex]
So, the expression for [tex]\( (f+g)(x) \)[/tex] is [tex]\( 3^x + 12x - 4 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( 3^x + 12 x - 4 \)[/tex]
