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f (x + y) – f (x) – f (y) = x y + 1

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by sanju09 » Mon May 10, 2010 12:02 am
A real valued function f (x) is such that f (x + y) - f (x) - f (y) = x y + 1 for real x and y. If f (−2) = −2, then what is the value of f (3)?
(A) −2
(B) 0
(C) 2
(D) 4
(E) 8
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by firdaus117 » Mon May 10, 2010 8:07 am
Putting x=-2 & y=0, we get f(0)=-1
Putting x=-2 & y=2, we get f(2)= 4
Putting x=1 & y=1,we get f(1)= 1
[spoiler]Finally putting x=1 & y=2,we get f(3)= 8
Option E[/spoiler]
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by liferocks » Mon May 10, 2010 8:15 am
f(x+y)=f(x)+f(y)+xy+1

now for x=y=-1
f(-2)=2f(-1)+2=-2 or f(-1)=-2

for x=y=0
f(0)=2f(0)+1 or f(0)=-1

for x=1,y=-1
f(0)=f(1)+f(-1)-1+1 or -1=f(1)-2 or f(1)=1

for x=2 y=-2
f(0)=f(2)+f(-2)-4+1 or f(2)=4

for x=2 and y=1
f(3)=f(2)+f(1)+2+1=4+1+2+1=8

Ans option E
"If you don't know where you are going, any road will get you there."
Lewis Carroll
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