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.