This is what I do not understand.
You are given a tetrahedron and asked to determine if a point is inside?
You cannot, because it can be inside or outside.
Or are you given a certain tetrahedron surface defined as,
And you are given P(x_0,y_0,z_0)
And asked to determine if P is inside f?
It looks very similar to that polygon test (whatever it is called) for 2-d.