前不久,在函数复习中有下面的问题:已知f(x)为偶函数,当x≥0时,f(x)=2a|x-1|-a(a>0),若函数y=f[f(x)]恰有10个零点,则a的取值范围为().(A)(0,1/2)(B)(1/2,1/3)(C)(0,1/2](D)[3/2,+∞)分析这是一类特殊的复合函数,就是以自身为中间变量构成的复合函数,即y=f(f(x)),我把它称之为“自身复合函数”.显然,自身复合函数的内函数和外函数有相同的图像. Not long ago, there were the following problems in function review: It is known that f (x) is an even function, and when x≥0, f (x) = 2a | x-1 | -a (a> 0) = f [f (x)] has exactly 10 zeros, then the range of a is () (A) (0,1 / 2) (B) (1/2, 1/3) 0,1 / 2] (D) [3/2, + ∞) Analysis This is a special type of complex function, which is a complex function composed of itself as an intermediate variable, that is, y = f Call it “autocompletion function.” Obviously, the intrinsic and extrinsic functions of the autochip have the same image.