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).

(In reply to

True story by Jer)

Now that's funny! I think the problem is better which two pieces, since solving the first easy part can get get you off on the wrong start for the second part.