题目

已知定义在R上的函数Y=F(X)对任意实数X满足1FX=F(-X) 2 F(-X+派）=FX且当X属于O,派/2时 FX=SINX 求F(-7派/
派求F(-7派/3）的值

提问时间：2020-10-31

答案

因为f(-x)=f(x),且f(-x+π)=f(x)
所以f(-x)=f(-x+π)
f(-7π/3)=f(-7π/3+π)=f(-7π/3+π+π)=f(-π/3)
因为f(-x)=f(x),所以f(-π/3)=f(π/3)
0＜π/3＜π/2,所以,f(π/3)=sin(π/3)=√3/2