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03 May 2007, 06:43
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Pls see attached. For me it seems to be a very confusing problem 
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Thank you for understanding, and happy exploring!
The best way is to calculate f(a+b) and then f(a) + f(b). Normally, u would be able to conclude it wihout other calculations than moral ones 
1) f(x) = x^2
implies that:
o f(a+b) = (a+b)^2
= a^2 + b^2 + 2*a*b
(= f(a) + f(b) + 2*f(a)/a * (f(b)/b) if a & b are different from 0
)
o f(a) + f(b) = a^2 + b^2
Thus, f(a+b) != f(a) + f(b)
2) f(x) = x+1
implies that:
o f(a+b) = (a+b) + 1
= a + b + 1
(= f(a) + f(b) - 1)
o f(a) + f(b) = (a + 1) + (b+1) = a + b + 2
Thus, f(a+b) != f(a) + f(b)
3) f(x) = sqrt(x)
implies that:
o f(a+b) = sqrt(a+b)
o f(a) + f(b) = sqrt(a) + sqrt(b)
Thus, f(a+b) != f(a) + f(b)
4) f(x) = 2/x
implies that:
o f(a+b) = 2/(a+b)
o f(a) + f(b) = 2/a + 2/b
Thus, f(a+b) != f(a) + f(b)
5) f(x) = -3*x
implies that:
o f(a+b) = -3*(a+b)
= -3*a -3*b
o f(a) + f(b) = (-3*a) + (-3*b)
= -3*a -3*b
Bingo !
1) f(x) = x^2
implies that:
o f(a+b) = (a+b)^2
= a^2 + b^2 + 2*a*b
(= f(a) + f(b) + 2*f(a)/a * (f(b)/b) if a & b are different from 0
)
o f(a) + f(b) = a^2 + b^2
Thus, f(a+b) != f(a) + f(b)
2) f(x) = x+1
implies that:
o f(a+b) = (a+b) + 1
= a + b + 1
(= f(a) + f(b) - 1)
o f(a) + f(b) = (a + 1) + (b+1) = a + b + 2
Thus, f(a+b) != f(a) + f(b)
3) f(x) = sqrt(x)
implies that:
o f(a+b) = sqrt(a+b)
o f(a) + f(b) = sqrt(a) + sqrt(b)
Thus, f(a+b) != f(a) + f(b)
4) f(x) = 2/x
implies that:
o f(a+b) = 2/(a+b)
o f(a) + f(b) = 2/a + 2/b
Thus, f(a+b) != f(a) + f(b)
5) f(x) = -3*x
implies that:
o f(a+b) = -3*(a+b)
= -3*a -3*b
o f(a) + f(b) = (-3*a) + (-3*b)
= -3*a -3*b
Bingo !
03 May 2007, 07:40
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Thank you, Fig! You are like the light at the end of the tunnel! 
Please advise should we generally guess on such problems? Is it worth spending 3-3.5 minutes on calculations if such a problem is tossed at the end of the quant section?
Please advise should we generally guess on such problems? Is it worth spending 3-3.5 minutes on calculations if such a problem is tossed at the end of the quant section? 
Please advise should we generally guess on such problems? Is it worth spending 3-3.5 minutes on calculations if such a problem is tossed at the end of the quant section?
... Thanks for it 
