Question

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

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

$-h$

$0$

$h$

$2h$

$h^3$

先计算内层的 $h \otimes h$ 。

First evaluate the inner $h \otimes h$

$h \otimes h = h^3 - h$ ，然后再次应用这个运算。

$h \otimes h = h^3 - h,$ then apply the operation again

内层运算给出 $h \otimes h = h^3 - h$ 。因此 $\begin{aligned} h \otimes (h^3 - h) &= h^3 - (h^3 - h) \\ &= h \end{aligned}\text{。}$

所以正确答案是 C。

The inner operation gives $h \otimes h = h^3 - h.$ Then $\begin{aligned} h \otimes (h^3 - h) &= h^3 - (h^3 - h) \\ &= h. \end{aligned}$

Thus, the correct answer is C.