Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.