I think I might have answered my own question. I will try to post a picture...

\$$f : P \rightarrow Q \$$ and \$$g : P \leftarrow Q \$$

\$$g(q_1) = \bigvee \\{ p_1 \\} = p1 \$$

\$$g(q_{21}) = \bigvee \\{ p_1, p_{21}, p_{22}, p_{32}\\} = p_{32} \$$

\$$g(q_{22}) = \bigvee \\{ p_1, p_{21}, p_{22}, p_{31} \\} = p_{31} \$$