- View SourceDear 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 - View Sourcehii 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.

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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.

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