设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,f(cos^2θ+2msinθ)+f(-2m-2)
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![设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,f(cos^2θ+2msinθ)+f(-2m-2)](/uploads/image/z/1731002-50-2.jpg?t=%E8%AE%BE%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BAR+%E7%9A%84%E5%A5%87%E5%87%BD%E6%95%B0y%3Df%28x%29%E6%98%AF%E5%87%8F%E5%87%BD%E6%95%B0%2C%E8%8B%A5%E5%BD%930%E2%89%A4%CE%B8%E2%89%A4%CF%80%2F2%E6%98%AF%E6%97%B6%2C%E8%AE%BE%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BAR+%E7%9A%84%E5%A5%87%E5%87%BD%E6%95%B0y%3Df%28x%29%E6%98%AF%E5%87%8F%E5%87%BD%E6%95%B0%2C%E8%8B%A5%E5%BD%930%E2%89%A4%CE%B8%E2%89%A4%CF%80%2F2%E6%98%AF%E6%97%B6%2Cf%28cos%5E2%CE%B8%2B2msin%CE%B8%29%2Bf%28-2m-2%29)
设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,f(cos^2θ+2msinθ)+f(-2m-2)
设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,
设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,f(cos^2θ+2msinθ)+f(-2m-2)
设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,设定义域为R 的奇函数y=f(x)是减函数,若当0≤θ≤π/2是时,f(cos^2θ+2msinθ)+f(-2m-2)
f((cosθ)^2+2msinθ)+f(-2m-2)<0
f((cosθ)^2+2msinθ)<-f(-2m-2)
f(1-(sinθ)^2+2msinθ)
(sinθ-m)^2-m^2+2m+1>0
设:t=sinθ,则t∈[0,1]
设:g(t)=(t-m)^2-m^2+2m+1
①当m<0时,g(t)≥g(0)=2m+1
2m+1>0,解得m>-1/2
所以-1/2
-m^2+2m+1>0,解得1-√2
③当m>1时,g(t)≥g(1)=2
显然2>0成立
所以m>1
综上所述,m>-1/2