To determine [tex]\((f+g)(x)\)[/tex], we need to add the given functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
Given:
[tex]\[ f(x) = 3^x + 10x \][/tex]
[tex]\[ g(x) = 5x - 3 \][/tex]
The function [tex]\((f+g)(x)\)[/tex] is found by adding the two functions together:
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]
Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into the equation:
[tex]\[ (f+g)(x) = (3^x + 10x) + (5x - 3) \][/tex]
Now, combine like terms:
[tex]\[ (f+g)(x) = 3^x + 10x + 5x - 3 \][/tex]
[tex]\[ (f+g)(x) = 3^x + 15x - 3 \][/tex]
Thus, the correct expression for [tex]\((f+g)(x)\)[/tex] is:
[tex]\[ (f+g)(x) = 3^x + 15x - 3 \][/tex]
Therefore, the correct answer is:
C. [tex]\(3^x + 15x - 3\)[/tex]
