A thin equilateral triangular block of side length 1 unit has its face in the vertical xy-plane with a vertex Vat the origin. Under the influence of gravity, it will rotate about V until a side hits the x-axis floor (Figure 16). Let x denote the initial x-coordinate of the midpoint Al of the side opposite V, and let f(x) de-note the final x-coordinate of this point. Assume that the block balances when M is directly above V.
(a) Determine the domain and range of f.
(b) Where on this domain is /discontinuous?
(c) Identify any fixed points of f (see Problem 59).

-I -I Fix) Initial position Final position