如题一中的函数如何化简呢1.(2011·新课标全国)设函数f(x)=sin(ωx+φ)+cos(ωx+φ)的最小正周期为π,且f(-x)=f(x),则().A.f(x)在单调递减B.f(x)在单调递减C.f(x)在单调递增D.f(x)在单调递增
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 03:46:40
![如题一中的函数如何化简呢1.(2011·新课标全国)设函数f(x)=sin(ωx+φ)+cos(ωx+φ)的最小正周期为π,且f(-x)=f(x),则().A.f(x)在单调递减B.f(x)在单调递减C.f(x)在单调递增D.f(x)在单调递增](/uploads/image/z/4019217-33-7.jpg?t=%E5%A6%82%E9%A2%98%E4%B8%80%E4%B8%AD%E7%9A%84%E5%87%BD%E6%95%B0%E5%A6%82%E4%BD%95%E5%8C%96%E7%AE%80%E5%91%A21%EF%BC%8E%282011%C2%B7%E6%96%B0%E8%AF%BE%E6%A0%87%E5%85%A8%E5%9B%BD%29%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%EF%BC%9Dsin%28%CF%89x%EF%BC%8B%CF%86%29%EF%BC%8Bcos%28%CF%89x%EF%BC%8B%CF%86%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E4%B8%BA%CF%80%2C%E4%B8%94f%28%EF%BC%8Dx%29%EF%BC%9Df%28x%29%2C%E5%88%99%28%29%EF%BC%8EA%EF%BC%8Ef%28x%29%E5%9C%A8%E5%8D%95%E8%B0%83%E9%80%92%E5%87%8FB%EF%BC%8Ef%28x%29%E5%9C%A8%E5%8D%95%E8%B0%83%E9%80%92%E5%87%8FC%EF%BC%8Ef%28x%29%E5%9C%A8%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9ED%EF%BC%8Ef%28x%29%E5%9C%A8%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E)
如题一中的函数如何化简呢1.(2011·新课标全国)设函数f(x)=sin(ωx+φ)+cos(ωx+φ)的最小正周期为π,且f(-x)=f(x),则().A.f(x)在单调递减B.f(x)在单调递减C.f(x)在单调递增D.f(x)在单调递增
如题一中的函数如何化简呢
1.(2011·新课标全国)设函数f(x)=sin(ωx+φ)+cos(ωx+φ)的最小正周期为π,且f(-x)=f(x),则().
A.f(x)在单调递减
B.f(x)在单调递减
C.f(x)在单调递增
D.f(x)在单调递增
2.(2013·西安调研)设f(x)为定义在R上的奇函数,且当x≥0时,f(x)单调递减,若x1+x2>0,则f(x1)+f(x2)的值().
A.恒为正值 B.恒等于零
C.恒为负值 D.无法确定正负
请把过程也写出来,
如题一中的函数如何化简呢1.(2011·新课标全国)设函数f(x)=sin(ωx+φ)+cos(ωx+φ)的最小正周期为π,且f(-x)=f(x),则().A.f(x)在单调递减B.f(x)在单调递减C.f(x)在单调递增D.f(x)在单调递增
1
f(x)=sin(ωx+φ)+cos(ωx+φ)
=√2[√2/2*sin(ωx+φ)+√2/2cos(ωx+φ)]
=√2sin(wx+φ+π/4)
由2π/w=π得,w=2
∴f(x)=√2sn(2x+φ+π/4)
∵f(-x)=f(x)
∴f(x)是偶函数,图像关于y轴对称
那么x=0时,f(0)为最值
即sin(φ+π/4)=±1
∴φ+π/4=kπ+π/2,kπ∈Z
∴φ=kπ+π/4,k∈Z
k=0时,取φ=π/4
∴f(x)=√2sin(2x+π/2)=√2cos2x
至于选项,条件输入不全,无法判断
2.
设f(x)为定义在R上的奇函数,
且当x≥0时,f(x)单调递减,
那么x0
∴x1>-x2
∴f(x1)