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问题: 比较大小

已知函数Y=f(x)对任意实数都有f(-x)=f(x),f(x)=-f(x+1)且在[0,1]上单调递减,则比较大小:f(7/2) f(7/3) f(7/5)

解答:

f(7/2)=f(-7/2)=-f(-5/2)=f(-3/2)=-f(-1/2)=f(1/2)
f(7/3)=f(-7/3)=-f(-4/3)=f(-1/3)=f(1/3)
f(7/5)=f(-7/5)=-f(-2/5)=f(3/5)
然后就比较了