作业帮已知函数f(x)=cos²x,g(x)=1+1/2sin2x(1)若点A(a,y)(a∈[0,π/4])为函数f(x)与g(x)的图像的公共点(2)设x=x0是函数y=f(x)的图像的一条对称轴,求g(2x0)的值(3)求函数h(x)=f(x)+g(x),x∈[0,π/4]的值域
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![已知函数f(x)=cos²x,g(x)=1+1/2sin2x(1)若点A(a,y)(a∈[0,π/4])为函数f(x)与g(x)的图像的公共点(2)设x=x0是函数y=f(x)的图像的一条对称轴,求g(2x0)的值(3)求函数h(x)=f(x)+g(x),x∈[0,π/4]的值域](/uploads/image/z/2669411-11-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dcos%26%23178%3Bx%2Cg%28x%29%3D1%2B1%2F2sin2x%281%29%E8%8B%A5%E7%82%B9A%28a%2Cy%29%28a%E2%88%88%5B0%2C%CF%80%2F4%5D%29%E4%B8%BA%E5%87%BD%E6%95%B0f%28x%29%E4%B8%8Eg%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E7%9A%84%E5%85%AC%E5%85%B1%E7%82%B9%282%29%E8%AE%BEx%3Dx0%E6%98%AF%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E7%9A%84%E4%B8%80%E6%9D%A1%E5%AF%B9%E7%A7%B0%E8%BD%B4%2C%E6%B1%82g%282x0%29%E7%9A%84%E5%80%BC%283%29%E6%B1%82%E5%87%BD%E6%95%B0h%28x%29%3Df%28x%29%2Bg%28x%29%2Cx%E2%88%88%5B0%2C%CF%80%2F4%5D%E7%9A%84%E5%80%BC%E5%9F%9F)
已知函数f(x)=cos²x,g(x)=1+1/2sin2x(1)若点A(a,y)(a∈[0,π/4])为函数f(x)与g(x)的图像的公共点(2)设x=x0是函数y=f(x)的图像的一条对称轴,求g(2x0)的值(3)求函数h(x)=f(x)+g(x),x∈[0,π/4]的值域
已知函数f(x)=cos²x,g(x)=1+1/2sin2x
(1)若点A(a,y)(a∈[0,π/4])为函数f(x)与g(x)的图像的公共点
(2)设x=x0是函数y=f(x)的图像的一条对称轴,求g(2x0)的值
(3)求函数h(x)=f(x)+g(x),x∈[0,π/4]的值域
已知函数f(x)=cos²x,g(x)=1+1/2sin2x(1)若点A(a,y)(a∈[0,π/4])为函数f(x)与g(x)的图像的公共点(2)设x=x0是函数y=f(x)的图像的一条对称轴,求g(2x0)的值(3)求函数h(x)=f(x)+g(x),x∈[0,π/4]的值域
(1)
f(x)=cos²x
g(x)=1+(1/2)sin2x
f(x)=g(x)
(cosx)^2 =1+(1/2)sin2x
(cos2x +1)/2 = 1+(1/2)sin2x
sin2x- cos2x + 1 =0
√2sin(2x-π/4) =-1
2x-π/4 = -π/4
x = 0
ie a=0
(2)
y=f(x)
= (cosx)^2
(cos(x+x0))^2 = (cos(x-x0))^2
put x=x0
(cos(2x0))^2 = 1
2x0 = kπ
g(2x0) = 1+ (1/2)sin(kπ)
=1
(3)
h(x) =f(x) +g(x)
= (cosx)^2+ 1+(1/2)sin2x
= (1/2 )cos2x+(1/2)sin2x + 3/2
= (√2/2)(sin2x+π/4) + 3/2
h(x) :x∈[0,π/4]的值域
=[3/2,3/2+√2/2]