To find \((f+g)(x)\), we need to combine the functions \(f(x)\) and \(g(x)\).
We are given:
[tex]\[ f(x) = 7x - 3 \][/tex]
[tex]\[ g(x) = x^2 + 4x + 8 \][/tex]
The combined function \((f+g)(x)\) is simply the sum of \(f(x)\) and \(g(x)\):
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]
Let's add the two functions together:
[tex]\[ (f+g)(x) = (7x - 3) + (x^2 + 4x + 8) \][/tex]
Combine like terms:
[tex]\[ (f+g)(x) = x^2 + 4x + 7x + 8 - 3 \][/tex]
[tex]\[ (f+g)(x) = x^2 + 11x + 5 \][/tex]
Now we need to compare this with the given choices:
A. \((f+g)(x) = x^2 - 3x - 5\)
B. \((f+g)(x) = x^2 + 3x - 11\)
C. \((f+g)(x) = 8x^2 + 4x - 11\)
D. \((f+g)(x) = x^2 + 17x + 5\)
From our calculations, we have \((f+g)(x) = x^2 + 11x + 5\). Comparing this with the choices, it matches none of them perfectly.
Therefore, none of the given options A, B, C, or D are correct.
