Question

对正数 $x$ 和 $y$ ，运算 $\spadesuit (x,y)$ 定义为求 $\spadesuit (2,\spadesuit (2,2))$ 。 $\spadesuit (x,y) = x-\dfrac{1}{y}$

For positive numbers $x$ and $y$ the operation $\spadesuit (x,y)$ is defined as $\spadesuit (x,y) = x-\dfrac{1}{y}$ What is $\spadesuit (2,\spadesuit (2,2))?$

$\dfrac{2}{3}$

$1$

$\dfrac{4}{3}$

$\dfrac{5}{3}$

$2$

答案：C

知识点：自定义运算分数

难度评级：1020

解答：

先计算内层：因此 $\spadesuit (2, 2) = 2 - \dfrac{1}{2} = \dfrac{3}{2}.$ $\spadesuit \left(2, \dfrac{3}{2}\right) = 2 - \dfrac{1}{\frac{3}{2}} = \dfrac{4}{3}.$

所以正确答案是 C。

Evaluating the inner expression, we get $\spadesuit (2, 2) = 2 - \dfrac{1}{2} = \dfrac{3}{2}.$ Then we have $\spadesuit \left(2, \dfrac{3}{2}\right) = 2 - \dfrac{1}{\frac{3}{2}} = \dfrac{4}{3}.$

Thus, C is the correct answer.

2010 AMC 10A 第 6 题

答案：C

难度评级：1020

解答：

其他年份的第 6 题