New Batches at TathaGat Delhi & Noida!               Directions to CP centre
Some questions from FUNCTIONS.........help needed
by Nakul Kothari - Saturday, 1 August 2009, 12:00 AM
  Q  1- If f(x) is a function satisfying f(x).f(1/x)=f(x)+f(1/x) and f(4)=65 , waht will be the value of f(6)...?

Q 2- If f(x)=1/g(x) , then which of the following is correct?
a) f(f(g(f(x)))) = f(g(g(f(f(X)))))
b) f(g(g(f(f(x))))) = f(f(g(g(g(x)))))
c) g(g(f(f(g(f(x)))))) = f(f(g(g(f(g(x))))))
d) f(g(g(g(f(x))))) = g(g(f(f(f(x)))))


In both the cases please post the approach as I am not getting the clue to even start the ques.
Re: Some questions from FUNCTIONS.........help needed
by Sarvesh Kumar - Saturday, 1 August 2009, 05:43 PM
 

Q  1- If f(x) is a function satisfying f(x).f(1/x)=f(x)+f(1/x) and f(4)=65 , waht will be the value of f(6)...?

Ans:     f(6) = 6^3 +1 = 217



Q 2- If f(x)=1/g(x) , then which of the following is correct?
a) f(f(g(f(x)))) = f(g(g(f(f(X)))))
b) f(g(g(f(f(x))))) = f(f(g(g(g(x)))))
c) g(g(f(f(g(f(x)))))) = f(f(g(g(f(g(x))))))
d) f(g(g(g(f(x))))) = g(g(f(f(f(x)))))

Ans:   c) g(g(f(f(g(f(x)))))) = f(f(g(g(f(g(x)))))). 

Re: Some questions from FUNCTIONS.........help needed
by Himanshu Shekhar - Saturday, 1 August 2009, 10:00 PM
  Given f(x).f(1/x) = f(x) + f (1/x) and f(4) = 65. If f(x) = (x^n) + 1, given condition of the problem is satisfied. As f(4) = 65, n = 3 and f(x) = x^3+1. So, f(6) = 6^3+1 = 217.
Re: Some questions from FUNCTIONS.........help needed
by Nakul Kothari - Saturday, 1 August 2009, 11:25 PM
  thanks buddies but still i couldn't approach the question...please solve in detail

@ Himanshu Shekhar
I couldn't understand how you used the condition "f(x) = (x^n) + 1"
Re: Some questions from FUNCTIONS.........help needed
by puneet jain - Sunday, 2 August 2009, 03:53 AM
  f(X).f(1/X)=f(X)+f(1/X)
ie f(x)= f(1/x).(f(x)-1)
ie f(1/x)= f(x)/(f(x)-1)
putting f(4)=65=64+1 ---------- 1
we have f(1/4)=65/64= 1/64 + 1 --------- 2

frm 1 & 2.
f(x)= x^3+1
rest u know...
Re: Some questions from FUNCTIONS.........help needed
by userdce . - Sunday, 2 August 2009, 01:23 PM
  you are right nakul that it is difficult to come to conclusion that why
"f(x) = (x^n) + 1"
basically 65 is bit helpful as 4^3+1=65
also if we calculate f(1)
f(1)*f(1)=f(1)+f(1) ie f(1)=0,2
f(x) satisfies values of f(1) too



Re: Some questions from FUNCTIONS.........help needed
by Nakul Kothari - Monday, 3 August 2009, 12:11 AM
  fabulous approach....thanks guys !!!!!

What's the approach used in II ques.
Q 2- If f(x)=1/g(x) , then which of the following is correct?
a) f(f(g(f(x)))) = f(g(g(f(f(X)))))
b) f(g(g(f(f(x))))) = f(f(g(g(g(x)))))
c) g(g(f(f(g(f(x)))))) = f(f(g(g(f(g(x))))))
d) f(g(g(g(f(x))))) = g(g(f(f(f(x)))))

Re: Some questions from FUNCTIONS.........help needed
by DEBOLEENA MONDAL - Saturday, 16 August 2014, 10:45 AM
  since f(x) & g(x) are inverse of each other..equal no of f & g functions need to be present on either side..only option c satisfies this..