已知函数f(x)=2sin(-3x+π/4),高手快来已知函数f(x)=2sin(-3x+π/4)(1)求f(x)的单调递增区间(这一题仅供参考下题,可以不做)(2)当f(x)大于等于根号2时,求x的取值范围(答案是[π/2+2kπ/3,2π/3+2kπ/3]
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![已知函数f(x)=2sin(-3x+π/4),高手快来已知函数f(x)=2sin(-3x+π/4)(1)求f(x)的单调递增区间(这一题仅供参考下题,可以不做)(2)当f(x)大于等于根号2时,求x的取值范围(答案是[π/2+2kπ/3,2π/3+2kπ/3]](/uploads/image/z/1858778-26-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%28-3x%2B%CF%80%2F4%29%2C%E9%AB%98%E6%89%8B%E5%BF%AB%E6%9D%A5%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%28-3x%2B%CF%80%2F4%29%EF%BC%881%EF%BC%89%E6%B1%82f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4%EF%BC%88%E8%BF%99%E4%B8%80%E9%A2%98%E4%BB%85%E4%BE%9B%E5%8F%82%E8%80%83%E4%B8%8B%E9%A2%98%2C%E5%8F%AF%E4%BB%A5%E4%B8%8D%E5%81%9A%EF%BC%89%EF%BC%882%EF%BC%89%E5%BD%93f%28x%29%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E%E6%A0%B9%E5%8F%B72%E6%97%B6%2C%E6%B1%82x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%EF%BC%88%E7%AD%94%E6%A1%88%E6%98%AF%5B%CF%80%2F2%2B2k%CF%80%2F3%2C2%CF%80%2F3%2B2k%CF%80%2F3%5D)
已知函数f(x)=2sin(-3x+π/4),高手快来已知函数f(x)=2sin(-3x+π/4)(1)求f(x)的单调递增区间(这一题仅供参考下题,可以不做)(2)当f(x)大于等于根号2时,求x的取值范围(答案是[π/2+2kπ/3,2π/3+2kπ/3]
已知函数f(x)=2sin(-3x+π/4),高手快来
已知函数f(x)=2sin(-3x+π/4)
(1)求f(x)的单调递增区间(这一题仅供参考下题,可以不做)
(2)当f(x)大于等于根号2时,求x的取值范围(答案是[π/2+2kπ/3,2π/3+2kπ/3](k∈Z)怎么做?谢谢
已知函数f(x)=2sin(-3x+π/4),高手快来已知函数f(x)=2sin(-3x+π/4)(1)求f(x)的单调递增区间(这一题仅供参考下题,可以不做)(2)当f(x)大于等于根号2时,求x的取值范围(答案是[π/2+2kπ/3,2π/3+2kπ/3]
(1)f(x)=2sin(-3x+π/4)=-2sin(3x-π/4)
∵2kπ+π/2≤3x-π/4≤2kπ+2π/3,k∈Z
∴2kπ/3+π/4≤x≤5π/12+2kπ/3,k∈Z
∴f(x)的单调递增区间[2kπ/3+π/4,5π/12+2kπ/3],k∈Z
(2)∵f(x)=-2sin(3x-π/4)≥√2
∴sin(3x-π/4)≤-√2/2
∴2kπ-3π/4≤3x-π/4≤2kπ-π/4,k∈Z(根据正弦函数图像)
∴2kπ/3-π/6≤x≤2kπ/3,k∈Z(做到这步结尾也正确)
由于此函数周期为2π/3,所以将不等式两边同时加2π/3即得π/2+2kπ/3≤x≤2π/3+2kπ/3,k∈Z
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