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[tex]\[
\begin{array}{ll}
f(x) = x^2 + 1 & g(x) = 5 - x \\
(f + g)(x) = & \\
\end{array}
\][/tex]

A. [tex]\( x^2 + x - 4 \)[/tex]

B. [tex]\( x^2 + x + 4 \)[/tex]

C. [tex]\( x^2 - x + 6 \)[/tex]

D. [tex]\( x^2 + x + 6 \)[/tex]

Sagot :

GinnyAnsweridn
To solve this problem, we first need to define the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:

[tex]\[ f(x) = x^2 + 1 \][/tex]
[tex]\[ g(x) = 5 - x \][/tex]

Next, we need to find the value of [tex]\((f + g)(x)\)[/tex], which is the sum of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:

[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]

Substituting the given functions into this expression:

[tex]\[ (f + g)(x) = (x^2 + 1) + (5 - x) \][/tex]

Now, let's combine the like terms:

[tex]\[ (f + g)(x) = x^2 + 1 + 5 - x \][/tex]
[tex]\[ (f + g)(x) = x^2 - x + 6 \][/tex]

Therefore, the simplified expression for [tex]\((f + g)(x)\)[/tex] is:

[tex]\[ \boxed{x^2 - x + 6} \][/tex]

So, the correct answer from the given options is:

[tex]\[ x^2 - x + 6 \][/tex]
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