Because F(X) is an even function and G(X) is a odd function, so:

F(-X)-G(-X)= F(X)-[-G(X)]= F(X)+G(X)

So: f (-x)-g (-x) = (-x)? +(-X)-2= X？ -X-2=F(X)+G(X)

Then solve the equations according to the known and above two equations.

F(X)-G(X)=X？ +X-2 ①

F(X)+G(X)=X？ -X-2 ②

①+②: 2F(X)=2X？ -4 So F(X)=X? -2

Substitute ① to get: g (x) =-x.