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]
