As shown in the figure, in rectangle ABCD, ab = 3, BC = 4, e is the moving point on edge ad, f is a point on ray BC, EF = BF and intersecting ray DC at point G, let AE = x, BF = y (1) When △ bef is an equilateral triangle, find the length of BF (2) Find the analytic expression of the function between Y and X, and write out its domain of definition (3) Fold △ Abe along the straight line be, and point a falls at a '. Try to explore whether △ a'bf can be an isosceles triangle? If so, ask for the length of AE; if not, explain the reason As long as the answer and steps of the third question

As shown in the figure, in rectangle ABCD, ab = 3, BC = 4, e is the moving point on edge ad, f is a point on ray BC, EF = BF and intersecting ray DC at point G, let AE = x, BF = y (1) When △ bef is an equilateral triangle, find the length of BF (2) Find the analytic expression of the function between Y and X, and write out its domain of definition (3) Fold △ Abe along the straight line be, and point a falls at a '. Try to explore whether △ a'bf can be an isosceles triangle? If so, ask for the length of AE; if not, explain the reason As long as the answer and steps of the third question

Point a must fall on EF, then Y-X = 3, and then use the conclusion of the second question to do it. This is the case of possibility