To solve for [tex]\((f + g)(2)\)[/tex] given the functions [tex]\( f(x) = 2x^2 + 3x \)[/tex] and [tex]\( g(x) = x - 2 \)[/tex], follow these steps:
1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 2(2)^2 + 3(2)
\][/tex]
- Calculate [tex]\( (2)^2 \)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
- Multiply this by 2:
[tex]\[
2 \times 4 = 8
\][/tex]
- Multiply 3 by 2:
[tex]\[
3 \times 2 = 6
\][/tex]
- Add both results:
[tex]\[
8 + 6 = 14
\][/tex]
Therefore, [tex]\( f(2) = 14 \)[/tex].
2. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 2 \)[/tex]:
[tex]\[
g(2) = 2 - 2
\][/tex]
- Subtract 2 from 2:
[tex]\[
2 - 2 = 0
\][/tex]
Therefore, [tex]\( g(2) = 0 \)[/tex].
3. Add [tex]\( f(2) \)[/tex] and [tex]\( g(2) \)[/tex]:
[tex]\[
(f + g)(2) = f(2) + g(2)
\][/tex]
- Substitute [tex]\( f(2) \)[/tex] and [tex]\( g(2) \)[/tex]:
[tex]\[
(f + g)(2) = 14 + 0
\][/tex]
- Add the results:
[tex]\[
14 + 0 = 14
\][/tex]
Therefore, [tex]\((f + g)(2) = 14\)[/tex].
The correct answer is not provided directly among the options, but the result of [tex]\((f + g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].
