1
Ricky
·2010-05-29 10:00:49
Given ,
f ( x ) = f ( x + 1x + 2 )
Hence , x = x + 1x + 2
or , x 2 + 2 x = x + 1
or , x 2 + x - 1 = 0
So , x = - 1 ± √52
Again , as f ( x ) is an even function , hence ,
f ( - x ) = f ( x ) = f ( x + 1x + 2 )
or , - x = x + 1x + 2
or , x 2 + 2 x = - x - 1
or , x 2 + 3 x + 1 = 0
Hence , x = - 3 ± √52
So , we find out exactly 4 values of x .
1
Ricky
·2010-05-29 10:05:21
1 >
S = 11 + 12 + 13 + ....... + 12 n - 1 > 12 + 12 + 12 + ...... + 12 = n2
Again , S = 11 + 12 + 13 + ....... + 12 n - 1 < 11 + 11 + 11 + ...... + 11 = n
So , I guess the answer is B .
11
Devil
·2010-05-29 21:46:50
1) f(x)=f(y) does not necessarily mean x=±y as the only possibility.
1
Ricky
·2010-05-29 22:53:08
I agree with you , Soumik , the function should be either strictly increasing or strictly decreasing . I feel this is an old IIT - JEE question , isn ' t it ?
66
kaymant
·2010-05-30 10:19:09
@Ricky: " I feel this is an old IIT - JEE question , isn ' t it ?"
Does that change the basics?
1
Ricky
·2010-05-30 10:52:32
Of course no , sir . I did not at all wanted to give an impression that since the question is already a past IIT Qs . , so the concept is not correct . Actually , it ' s a part of my mistake , I should not have said it in the first place . Sorry , sir .
11
Devil
·2010-05-31 21:30:36
What Gallardo did was exactly what the book did (from which the qsn is given).
So did IIT gve an incomplete qsn in 1996 ?