Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
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]
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]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.