To find \((f + g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\).
Given:
[tex]\[ f(x) = 2x - 6 \][/tex]
[tex]\[ g(x) = 3x + 9 \][/tex]
Let's add \(f(x)\) and \(g(x)\):
[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
[tex]\[ (f + g)(x) = (2x - 6) + (3x + 9) \][/tex]
Combine the like terms:
[tex]\[ (f + g)(x) = 2x + 3x - 6 + 9 \][/tex]
[tex]\[ (f + g)(x) = 5x + 3 \][/tex]
Upon examining the given options:
A. \((f + g)(x) = 5x + 3\)
B. \((f + g)(x) = -x - 15\)
C. \((f + g)(x) = x + 15\)
D. \((f + g)(x) = 5x + 15\)
The correct answer is:
[tex]\[ A. (f + g)(x) = 5x + 3 \][/tex]
