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f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(...

`f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x).`
The value of f(3) is

A

1

B

0

C

-1

D

-2

Text Solution

AI Generated Solution

To solve for \( f(3) \) given the functions \( f(x) = x^2 + xg'(1) + g''(2) \) and \( g(x) = f(1)x^2 + xf'(x) + f'(x) \), we will follow these steps: ### Step 1: Define Variables Let \( g'(1) = a \) and \( g''(2) = b \). Thus, we can rewrite \( f(x) \) as: \[ f(x) = x^2 + ax + b \] ...
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