Question

if 2f(x)+3f(-x)=x2-x+1 then what is the value of f(x)

Answer 1

f(x) = ax² + bx + c 
f(-x) = ax² - bx + c 
2f(x) = 2ax² + 2bx + 2c 
3f(-x) = 3ax² - 3bx + 3c 
Equating x² terms: (2a+3a)x² = x² → a = ⅕ 
and 
x terms: (2b - 3b)x = -x → b = 1 
and 
constant: 5c = 1 → c = ⅕ 
that means f(x) = ⅕x² + x + ⅕ 
f '(x) = ⅖x + 1 → f '(1) = 7/5

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