已知函数f(x)对任意实数x都有f(-x)=f(x),f(x)=-f(x+1),且在[0,1]单调递减,比较f(7/2),f(-1/3),f(7/5)的大小.
问题描述:
已知函数f(x)对任意实数x都有f(-x)=f(x),f(x)=-f(x+1),且在[0,1]单调递减,比较f(7/2),f(-1/3),f(7/5)的大小.
答
f(7/2) = -f(5/2) = f(3/2) = -f(1/2) f(-1/3)= -f(1/3)f(7/5) = -f(2/5)因为在[0,1]单调递减所以f(1/2) -f(2/5) > -f(1/3)即 f(7/2) > f(7/5) > f(-1/3)