To solve the problem of finding [tex]\((f - g)(x)\)[/tex] given the functions [tex]\(f(x) = 3^x + 10x\)[/tex] and [tex]\(g(x) = 5x - 3\)[/tex], follow these steps:
1. Write down the given functions:
[tex]\(f(x) = 3^x + 10x\)[/tex]
[tex]\(g(x) = 5x - 3\)[/tex]
2. Set up the expression for [tex]\((f - g)(x)\)[/tex]:
[tex]\((f - g)(x) = f(x) - g(x)\)[/tex]
3. Substitute the given functions into the expression:
[tex]\[
(f - g)(x) = (3^x + 10x) - (5x - 3)
\][/tex]
4. Distribute the subtraction to each term in [tex]\(g(x)\)[/tex]:
[tex]\[
(f - g)(x) = 3^x + 10x - 5x + 3
\][/tex]
Here, we need to be careful with the negative sign when subtracting [tex]\(g(x)\)[/tex].
5. Combine like terms:
- Combine [tex]\(10x\)[/tex] and [tex]\(-5x\)[/tex]:
[tex]\[
10x - 5x = 5x
\][/tex]
- The constant term will simply be [tex]\(+3\)[/tex].
So, the simplified expression is:
[tex]\[
(f - g)(x) = 3^x + 5x + 3
\][/tex]
This matches option B. Therefore, the answer is:
[tex]\[
\boxed{3^x + 5x + 3}
\][/tex]
