Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

If [tex]\( f(x) = 2x^2 - 5 \)[/tex] and [tex]\( g(x) = 3x + 3 \)[/tex], find [tex]\((f - g)(x)\)[/tex].

A. [tex]\(3x - 2x^2 - 2\)[/tex]

B. [tex]\(2x^2 - 3x - 8\)[/tex]

C. [tex]\(-x^2 - 8\)[/tex]

D. [tex]\(2x^2 - 3x - 2\)[/tex]

Sagot :

GinnyAnswer
To solve the problem of finding [tex]\((f - g)(x)\)[/tex], where [tex]\(f(x) = 2 x^2 - 5\)[/tex] and [tex]\(g(x) = 3x + 3\)[/tex], we need to subtract the function [tex]\(g(x)\)[/tex] from the function [tex]\(f(x)\)[/tex]:

1. Write down the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ f(x) = 2x^2 - 5 \][/tex]
[tex]\[ g(x) = 3x + 3 \][/tex]

2. Subtract [tex]\(g(x)\)[/tex] from [tex]\(f(x)\)[/tex]:
[tex]\[ (f - g)(x) = f(x) - g(x) = (2x^2 - 5) - (3x + 3) \][/tex]

3. Distribute the negative sign through the expression [tex]\(g(x)\)[/tex]:
[tex]\[ (f - g)(x) = 2x^2 - 5 - 3x - 3 \][/tex]

4. Combine like terms:
[tex]\[ (f - g)(x) = 2x^2 - 3x - 8 \][/tex]

So, the function [tex]\((f - g)(x)\)[/tex] is:
[tex]\[ (f - g)(x) = 2x^2 - 3x - 8 \][/tex]

Thus, the correct answer is:

B. [tex]\(2x^2 - 3x - 8\)[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.