偶函数fx满足f(x+2)=f(x)对一切实数x成立,且当(-2013,-2012)偶函数f(x)满足:f(x+2)=f(x)对一切实数x成立,且当x∈(-2013,-2012)时,f(x)=cosπ/2x,f(-2012)=a,f(-2013)=b,a<b.(1)若△ABC是钝角三角形,C是钝角,证
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![偶函数fx满足f(x+2)=f(x)对一切实数x成立,且当(-2013,-2012)偶函数f(x)满足:f(x+2)=f(x)对一切实数x成立,且当x∈(-2013,-2012)时,f(x)=cosπ/2x,f(-2012)=a,f(-2013)=b,a<b.(1)若△ABC是钝角三角形,C是钝角,证](/uploads/image/z/5556127-31-7.jpg?t=%E5%81%B6%E5%87%BD%E6%95%B0fx%E6%BB%A1%E8%B6%B3f%28x%2B2%29%3Df%28x%29%E5%AF%B9%E4%B8%80%E5%88%87%E5%AE%9E%E6%95%B0x%E6%88%90%E7%AB%8B%2C%E4%B8%94%E5%BD%93%28-2013%2C-2012%29%E5%81%B6%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3%3Af%28x%2B2%29%3Df%28x%29%E5%AF%B9%E4%B8%80%E5%88%87%E5%AE%9E%E6%95%B0x%E6%88%90%E7%AB%8B%2C%E4%B8%94%E5%BD%93x%E2%88%88%28-2013%2C-2012%29%E6%97%B6%2Cf%28x%29%3Dcos%CF%80%2F2x%2Cf%EF%BC%88-2012%EF%BC%89%3Da%2Cf%EF%BC%88-2013%EF%BC%89%3Db%2Ca%EF%BC%9Cb.%EF%BC%881%EF%BC%89%E8%8B%A5%E2%96%B3ABC%E6%98%AF%E9%92%9D%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2%2CC%E6%98%AF%E9%92%9D%E8%A7%92%2C%E8%AF%81)
偶函数fx满足f(x+2)=f(x)对一切实数x成立,且当(-2013,-2012)偶函数f(x)满足:f(x+2)=f(x)对一切实数x成立,且当x∈(-2013,-2012)时,f(x)=cosπ/2x,f(-2012)=a,f(-2013)=b,a<b.(1)若△ABC是钝角三角形,C是钝角,证
偶函数fx满足f(x+2)=f(x)对一切实数x成立,且当(-2013,-2012)
偶函数f(x)满足:f(x+2)=f(x)对一切实数x成立,且当x∈(-2013,-2012)时,f(x)=cosπ/2x,f(-2012)=a,f(-2013)=b,a<b.
(1)若△ABC是钝角三角形,C是钝角,证明:f(sinA)>f(cosB)
(2)若f(x)的值域是【a,b】,求a,b的值,并求方程f(x)=b的解集
偶函数fx满足f(x+2)=f(x)对一切实数x成立,且当(-2013,-2012)偶函数f(x)满足:f(x+2)=f(x)对一切实数x成立,且当x∈(-2013,-2012)时,f(x)=cosπ/2x,f(-2012)=a,f(-2013)=b,a<b.(1)若△ABC是钝角三角形,C是钝角,证
(1)f(x)是周期为2的函数,因此易知x∈(-1,0)时,f(x)=cos(πx/2)
又f(x)是偶函数,因此当x∈(0,1)时,f(x)=cos(-πx/2)=cos(πx/2),此时f(x)是减函数
由于A、B都是锐角,因此sinA、cosB∈(0,1),且此时y=sinx是增函数
又A+B<π/2,易知sinA
(2)由(1)知,当x不是整数时,f(x)=cos(πx/2),此时的值域为(-1,1)
而当x∈Z时,f(x)∈{a,b}
因此若要当x∈R时f(x)的值域为[a,b],只能是a=-1、b=1,此时同样满足解析式f(x)=cos(πx/2)
∴当x∈R时,f(x)=cos(πx/2)
令f(x)=1,解得x=2k(k∈Z)
阿衰v型吧