Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

If [tex]f(x)=2x^2+1[/tex] and [tex]g(x)=x^2-7[/tex], find [tex](f+g)(x)[/tex].

A. [tex]x^2-6[/tex]
B. [tex]x^2+8[/tex]
C. [tex]3x^2+8[/tex]
D. [tex]3x^2-6[/tex]

Sagot :

GinnyAnswer
To determine [tex]\((f + g)(x)\)[/tex], we need to sum the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].

Given:
[tex]\[ f(x) = 2x^2 + 1 \][/tex]
[tex]\[ g(x) = x^2 - 7 \][/tex]

First, let's add these two functions together:

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

Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:

[tex]\[ (f + g)(x) = (2x^2 + 1) + (x^2 - 7) \][/tex]

Next, combine like terms:

[tex]\[ (f + g)(x) = 2x^2 + x^2 + 1 - 7 \][/tex]
[tex]\[ (f + g)(x) = 3x^2 - 6 \][/tex]

So, the resulting function is:

[tex]\[ (f + g)(x) = 3x^2 - 6 \][/tex]

Therefore, the correct answer is:

D. [tex]\(3x^2 - 6\)[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.