Question

the function f has the property that ,all non-zero real numbers f(x)+2f(1/x)=3x .how many non-zero real numbers solution are there to the equation f(x)=f(-x)

Answer 1

First of all, we can find f explicitly. Indeed, we have

f(x)+2f(1/x)f(1/x)+2f(x)=3x=3/x

which is a simple system of linear equations whose solution gives

f(x)=2x−x.

Hence, f(y)=f(−y) if and only if y=±root2