Let f : (0, 1/3 ] → R such that f (x) = x^2.Part 1: Show that f (x) < x.Part 2: Show that f has no fixed point on (0, 1/3 ]. Hint: Assume there were a point c in (0, 1/3 ]such that f (c) = c and derive a contradiction.Part 3: Show that the function f (x) = 1/(1+x^2) from [0, ∞) to [0, ∞) has a fixed point c. Hint: Setf (x) = x and show the resulting equation has a solution in [0, ∞) using the the IVP