奇函数f(x)的定义域为R,且在[0,+∞)上是增函数,当0≤θ≤π/2时,是否存在实数m,使f（4m-2mcosθ）-f（2sin²θ+2）＞f（0）对所有θ∈[0,π/2]求出所有适合条

题目

奇函数f(x)的定义域为R,且在[0,+∞)上是增函数,当0≤θ≤π/2时,是否存在实数m,使f（4m-2mcosθ）-f（2sin²θ+2）＞f（0）对所有θ∈[0,π/2]求出所有适合条件的实数m.

答案

f(0) = -f(0)=> f(0) = 0f（4m-2mcosθ）-f（2sin²θ+2）＞f（0）= 0=> f（4m-2mcosθ）> f（2sin²θ+2）0≤θ≤π/24m-2mcosθ > 0 and 2sin²θ+2 > 0=> 4m-2mcosθ > 2sin²θ+24m-2mcosθ > -...