2014 高考数学第 10 题答案解析

2014_退役省自主命题 (2014·文)

2014 ?? 第 10 题 单选题 区分题
2014_退役省自主命题 (2014·文)

10.已知 $f(x)$ 为偶函数,当 $x \geq 0$ 时,$f(x)=\left\{\begin{array}{c}\cos \pi x, x \in\left[0, \frac{1}{2}\right] \\ 2 x-1, x \in\left(\frac{1}{2},+\infty\right)\end{array}\right.$,则不等式 $f(x-1) \leq \frac{1}{2}$ 的解集为

A. $\left[\frac{1}{4}, \frac{2}{3}\right] \cup\left[\frac{4}{3}, \frac{7}{4}\right]$
B. $\left[-\frac{3}{4},-\frac{1}{3}\right] \cup\left[\frac{1}{4}, \frac{2}{3}\right]$
C. $\left[\frac{1}{3}, \frac{3}{4}\right] \cup\left[\frac{4}{3}, \frac{7}{4}\right]$
D. $\left[-\frac{3}{4},-\frac{1}{3}\right] \cup\left[\frac{1}{3}, \frac{3}{4}\right]$
参考答案A

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