[中學] 拋物線+合成函數
Q: Let f be a function such that the graph of f lies on a
parabola through (0,0) and (4,2). If funcution g is the
composition of f with itself, that is, g= f(f(x)), which
of the following points could lie on the graph of g?
(A) (1,1)
(B) (16,2)
(c) (8,8)
(D) either (A) or (B)
(E) either (B) or (C)
解答是E.
但是我覺得A應該也會在g上耶~
通過(0,0) and (4,2)的拋物線有兩種可能 : y=x^1/2 或 y=x^2/8
所以g可以是y=x^1/4, or y=x^4/512.
(B)在y=x^1/4, (C)在 y=x^4/512上，
但(1,1)應該也是在y=x^1/4上的吧(?)
可以麻煩大家幫忙確認一下嗎？ 謝謝!!
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