What are the coordinates of the points where f(x)=x^3-x^2+x+1
and g(x)=x^3+x^2+x-1 intersect?
well, that would be where
x^3-x^2+x+1 = x^3+x^2+x-1
2x^2-2 = 0
x = ±1
See
http://www.wolframalpha.com/input/?i=solve+x^3-x^2%2Bx%2B1+%3D+%28+x^3%2Bx^2%2Bx-1%29