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.

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Or are you given a certain tetrahedron surface defined as,

f(x,y,z)=C

And you are given P(x_0,y_0,z_0)

And asked to determine if P is inside f?

If so,

It looks very similar to that polygon test (whatever it is called) for 2-d.