已知f(x)=cos(2x-π/3)+sin²x-cosx(1)求f(x)周期及对称轴方程(2)g(x)=f²(x)+f(x),求g(x)值域
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![已知f(x)=cos(2x-π/3)+sin²x-cosx(1)求f(x)周期及对称轴方程(2)g(x)=f²(x)+f(x),求g(x)值域](/uploads/image/z/6893165-29-5.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3Dcos%282x-%CF%80%2F3%29%2Bsin%26%23178%3Bx-cosx%281%29%E6%B1%82f%28x%29%E5%91%A8%E6%9C%9F%E5%8F%8A%E5%AF%B9%E7%A7%B0%E8%BD%B4%E6%96%B9%E7%A8%8B%EF%BC%882%EF%BC%89g%EF%BC%88x%EF%BC%89%3Df%26%23178%3B%EF%BC%88x%EF%BC%89%2Bf%EF%BC%88x%EF%BC%89%2C%E6%B1%82g%EF%BC%88x%EF%BC%89%E5%80%BC%E5%9F%9F)
已知f(x)=cos(2x-π/3)+sin²x-cosx(1)求f(x)周期及对称轴方程(2)g(x)=f²(x)+f(x),求g(x)值域
已知f(x)=cos(2x-π/3)+sin²x-cosx
(1)求f(x)周期及对称轴方程
(2)g(x)=f²(x)+f(x),求g(x)值域
已知f(x)=cos(2x-π/3)+sin²x-cosx(1)求f(x)周期及对称轴方程(2)g(x)=f²(x)+f(x),求g(x)值域
f(x)=cos(2x-π/3)+sin²x-cos^2x
=1/2cos2x+√3/2sin2x-cos2x
=√3/2sin2x-1/2cos2x
=sin(2x-π/6)
f(x)周期T=2π/2=π
对称轴方程 2x-π/6=kπ+π/2 x=kπ/2+π/3
f(x)∈[-1,1]
令f(x)=t
y=t^2+t t∈[-1,1]
=(t+1/2)^2-1/4
当t=1时,ymax=2
当t=-1/2时 ,ymin=-1/4
g(x)值域[-1/4,2]