Answered

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If \( f(x) = 7x - 3 \) and \( g(x) = x^2 + 4x + 8 \), find \((f + g)(x)\).

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. [tex]\((f + g)(x) = x^2 + 17x + 5\)[/tex]

Sagot :

GinnyAnswer
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.
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