- Dear all,Could someone help me out in solving this problem-Let "f" be a function defined on the set of integers. Assume that "f" satisfies the following properties-f(0) ¹ 0f(1) = 3f(x) f(y) = f(x+y) + f(x-y)for all integers x & y.Q. What is the value of f(3)Options are 7, 18, 123, 322 & none of these.Q. What is the value of f(7)Options are 123, 322, 843, 1126 & none of these.Please tell me the best way to solve such kind of questions.Thanks in advance.regards,Avdhesh.

Did you know? You can CHAT without downloading messenger. Click here - hii hope this may help u...but 'm not sure whether this is d easiest way out..nywayswhen u put x=y=0..this gives eqn whose solution is f(0)= 0 or 2as its already stated that its not 0..it is 2;x=y[ {f(x)}^2-2] =f(2x) ... * (I)ny=1f(x+1)+f(x-1) =3f(x).... *(II)f(1) = 3f(2) = f(1)^2 - 2 =7 ....... by If(3) = 3f(2) - f(1) = 18 ....... by IIf(4) = 7^2 - 2= 47 ...... by If(6) = 18^2 - 2 = 322 ...... by If(8) = 47^2 - 2 = 2207 ....... by If(7) = 1/3 * (322 +2207) = 843 ......... by IIhence these are my solutions...correct me if i'm wrong..MKC
wrote:*YES <avdheshtomar@...>*Dear all,Could someone help me out in solving this problem-Let "f" be a function defined on the set of integers. Assume that "f" satisfies the following properties-f(0) ¹ 0f(1) = 3f(x) f(y) = f(x+y) + f(x-y)for all integers x & y.Q. What is the value of f(3)Options are 7, 18, 123, 322 & none of these.Q. What is the value of f(7)Options are 123, 322, 843, 1126 & none of these.Please tell me the best way to solve such kind of questions.Thanks in advance.regards,Avdhesh.

Did you know? You can CHAT without downloading messenger. Click here

Ready for the edge of your seat? Check out tonight's top picks on Yahoo! TV. My approach is as follows:

F(1,0) è f(1)*f(0) = f(1+0) + f(1-0)

3*f(0) = 2*3 è f(0) = 2

F(1,1) è f(1)*f(1) = f(1+1) + f(1-1)

3*3 = f(2) + 2 è f(2) = 7

F(2,1) è f(2)*f(1) = f(2+1) + f(2-1)

7*3 = f(3) + 3 è

**f(3) = 18**F(2,2) è f(2) * f(2) = f(2+2) + f(2-2)

7*7 = f(4) + 2 è f(4) = 47

F(4,3) è f(4) * f(3) = f(4+3) + f(4-3)

47*18 = f(7) + 3 è

**f(7) = 843****Regards,****Kunal Naik.****From:**ascent4cat@yahoogroups.com [mailto:ascent4cat@yahoogroups.com]**On Behalf Of**mahathi chitta

**Sent:**Thursday, August 16, 2007 11:20 PM

**To:**ascent4cat@yahoogroups.com

**Subject:**Re: [2IIM CAT Prep] please solve it !!!!!!!!!!!!hi

i hope this may help u...but 'm not sure whether this is d easiest way out..nyways

when u put x=y=0..this gives eqn whose solution is f(0)= 0 or 2

as its already stated that its not 0..it is 2;

x=y

[ {f(x)}^2-2] =f(2x) ... * (I)

n

y=1

f(x+1)+f(x-1) =3f(x).... *(II)

f(1) = 3

f(2) = f(1)^2 - 2 =7 ....... by I

f(3) = 3f(2) - f(1) = 18 ....... by II

f(4) = 7^2 - 2= 47 ...... by I

f(6) = 18^2 - 2 = 322 ...... by I

f(8) = 47^2 - 2 = 2207 ....... by I

f(7) = 1/3 * (322 +2207) = 843 ......... by II

hence these are my solutions... correct me if i'm wrong..

MKC

wrote:*YES <avdheshtomar@ yahoo.co. in>*Dear all,

Could someone help me out in solving this problem-

Let "f" be a function defined on the set of integers. Assume that "f" satisfies the following properties-

f(0) ¹ 0

f(1) = 3

f(x) f(y) = f(x+y) + f(x-y)

for all integers x & y.

Q. What is the value of f(3)

Options are 7, 18, 123, 322 & none of these.

Q. What is the value of f(7)

Options are 123, 322, 843, 1126 & none of these.

Please tell me the best way to solve such kind of questions.

Thanks in advance.

regards,

Avdhesh.

Did you know? You can CHAT without downloading messenger. Click here

Ready for the edge of your seat? Check out tonight's top picks on Yahoo! TV.

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