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For [tex]\( f(x) = 4x + 2 \)[/tex] and [tex]\( g(x) = x^2 - 6 \)[/tex], find [tex]\((f + g)(x)\)[/tex].

A. [tex]\( x^2 + 4x - 4 \)[/tex]
B. [tex]\( 4x^2 - 16 \)[/tex]
C. [tex]\( 4x^3 - 4 \)[/tex]
D. [tex]\( x^2 + 4x + 8 \)[/tex]

Sagot :

GinnyAnswer
To solve for [tex]\((f+g)(x)\)[/tex] given the functions [tex]\(f(x) = 4x + 2\)[/tex] and [tex]\(g(x) = x^2 - 6\)[/tex], we need to add the two functions together. The combined function [tex]\( (f+g)(x) \)[/tex] is simply:

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

Let’s substitute [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into the equation:

[tex]\[ (f+g)(x) = (4x + 2) + (x^2 - 6) \][/tex]

Now, combine like terms:

[tex]\[ (f+g)(x) = x^2 + 4x + 2 - 6 \][/tex]

Simplify the constant terms:

[tex]\[ (f+g)(x) = x^2 + 4x - 4 \][/tex]

Therefore, the combined function [tex]\((f+g)(x)\)[/tex] simplifies to:

[tex]\[ (f+g)(x) = x^2 + 4x - 4 \][/tex]

Thus, the correct answer is:

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