AMC12 2006 A

AMC12 2006 A · Q2

AMC12 2006 A · Q2. It mainly tests Functions basics.

Define $x\otimes y=x^3-y$. What is $h\otimes (h\otimes h)$?

定义$x\otimes y=x^3-y$。求$h\otimes (h\otimes h)$。

(A) $-h$ $-h$

(B) 0 0

(D) $2h$ $2h$

(E) $h^3$ $h^3$

Answer

Correct choice: (C)

正确答案：（C）

Solution

By the definition of $\otimes$, we have $h\otimes h=h^{3}-h$. Then, $h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=\boxed{\textbf{(C) }h}.$

由$\otimes$的定义可得$h\otimes h=h^{3}-h$。因此，$h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=\boxed{\textbf{(C) }h}.$

Topics

AL.010 Functions basics