Calculate f(f(x)) by yourself. Let's first discuss the size of x and 1/2 to remove the first absolute value. Then, when discussing the number of the second absolute value, the classification range of A is naturally obtained. ..

It can also be used as a graphic aid for analysis. F(x) is a tripod with a vertex of (1/2, a) and an opening of (0,0), f(f(x). ) = f(x.) is f (x). ) = f-(x.), f(x) intersects its inverse function f-(X), and is symmetrical about y = X. It is necessary to determine whether y = X is inside or outside the tripod, so it is necessary to discuss the sizes of a and 1/2. It can be seen directly from the drawing that only when A is greater than 1/2, will he intersect with the inverse function beyond the origin. Drawing is not rigorous in solving problems, but it can help to determine the scope of discussion.