A function f, defined for all non-zero real numbers x, satisfies:

f(x) + 4f(1/x) = 3x.

[1] Find all values of x for which f(x)=f(1/x);

[2] Find all values of x for which f(x)=f(-x).

The original problem as I found it had only part [2], when I typed it in I accidentally entered it wrong and for some reason put what is part [1].  When this was vetted in the queue someone suggested this was too easy and I should add part [2].  I did not notice my error at the time.  So by happy coincidence even though I entered the question wrong, it got fixed without my realizing it and we got an extra problem as well!

Posted by Jer on 2010-10-27 12:30:49