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If [tex]$f(x)=2x^2+3x$[/tex] and [tex]$g(x)=x-2$[/tex], what is [tex][tex]$(f+g)(2)$[/tex][/tex]?

A. 10
B.
C. 12
D. 10
E. [tex]$B$[/tex]

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Answer :

GinnyAnswer
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].

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