Define all functions that are defined in the set of real numbers excluding zero and satisfy the following:

f(x)+8f(1/x)-63x=0 , x≠0

f(x)+8f(1/x)=63x --(1)
Replace x by 1/x
f(1/x)+8f(x)=63/x

Multiply this with 8 and sub 1 from this eq, we get
63f(x)=63((8-x)/x²)
=> f(x)=(8-x)/x²; x≠0

Edited on September 27, 2007, 6:15 am

Posted by Praneeth on 2007-09-27 06:14:20