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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. 16
B. 14
C. 12
D. 10
E. 8

Sagot :

GinnyAnswer
Sure, let's determine [tex]\((f+g)(2)\)[/tex] given the functions [tex]\( f(x) = 2x^2 + 3x \)[/tex] and [tex]\( g(x) = x - 2 \)[/tex].

First, let's break down the process step-by-step:

Step 1: Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]

[tex]\[ f(2) = 2 \cdot (2)^2 + 3 \cdot (2) \][/tex]
[tex]\[ f(2) = 2 \cdot 4 + 6 \][/tex]
[tex]\[ f(2) = 8 + 6 \][/tex]
[tex]\[ f(2) = 14 \][/tex]

Step 2: Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 2 \)[/tex]

[tex]\[ g(2) = 2 - 2 \][/tex]
[tex]\[ g(2) = 0 \][/tex]

Step 3: Combine the results of [tex]\( f(2) \)[/tex] and [tex]\( g(2) \)[/tex] to find [tex]\((f+g)(2)\)[/tex]

[tex]\[ (f+g)(2) = f(2) + g(2) \][/tex]
[tex]\[ (f+g)(2) = 14 + 0 \][/tex]
[tex]\[ (f+g)(2) = 14 \][/tex]

So, the correct answer is [tex]\( \boxed{14} \)[/tex].
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