如果log1/2|x-π/3|≥log2(2/π)成立,那么sinx的取值范围是~A [-1/2,1/2]B [-1/2,1]C [-1/2,1/2)∪(1/2,1]D [-1/2,√3/2)]∪(√3/2,1]
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![如果log1/2|x-π/3|≥log2(2/π)成立,那么sinx的取值范围是~A [-1/2,1/2]B [-1/2,1]C [-1/2,1/2)∪(1/2,1]D [-1/2,√3/2)]∪(√3/2,1]](/uploads/image/z/3696617-65-7.jpg?t=%E5%A6%82%E6%9E%9Clog1%2F2%7Cx-%CF%80%2F3%7C%E2%89%A5log2%282%2F%CF%80%29%E6%88%90%E7%AB%8B%2C%E9%82%A3%E4%B9%88sinx%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%7EA+%5B-1%2F2%2C1%2F2%5DB+%5B-1%2F2%2C1%5DC+%5B-1%2F2%2C1%2F2%29%E2%88%AA%281%2F2%2C1%5DD+%5B-1%2F2%2C%E2%88%9A3%2F2%29%5D%E2%88%AA%28%E2%88%9A3%2F2%2C1%5D)
如果log1/2|x-π/3|≥log2(2/π)成立,那么sinx的取值范围是~A [-1/2,1/2]B [-1/2,1]C [-1/2,1/2)∪(1/2,1]D [-1/2,√3/2)]∪(√3/2,1]
如果log1/2|x-π/3|≥log2(2/π)成立,那么sinx的取值范围是~
A [-1/2,1/2]
B [-1/2,1]
C [-1/2,1/2)∪(1/2,1]
D [-1/2,√3/2)]∪(√3/2,1]
如果log1/2|x-π/3|≥log2(2/π)成立,那么sinx的取值范围是~A [-1/2,1/2]B [-1/2,1]C [-1/2,1/2)∪(1/2,1]D [-1/2,√3/2)]∪(√3/2,1]
解.log1/2|x-π/3|≥log2(2/π)=log1/2(π/2)
因为y=log1/2(x)在x>0上是个减函数,则有
|x-π/3|≤π/2
即-π/6≤x≤5π/6
则sinx的取值范围为[-1/2,1]
选B
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