函数F(X)的定义域为R,且满足F(X)是偶函数,F(X-1)是奇函数,若F(1)=9,则F(9)=?

Question

如题所述

Answer 1

f(x-1)是奇函数
f(-x-1)=-f(x-1)

f(x)是偶函数
f(-x)=f(x)

f(9)=f(-9)=f(-8-1)
=-f(8-1)
=-f(7)
=-f(-7)
=-f(-6-1)
=f(6-1)
=f(5)
=f(-5)
=f(-4-1)
=-f(4-1)
=-f(3)
=-f(-3)
=-f(-2-1)
=f(2-1)
=f(1)
=9

Answer 2

这种题 可以用图像解 适合题意的大都为 正弦或余弦图
这题为余弦 答案为9

Answer 3

F(9)=-F(-7)=-F(7)=F(-5)=F(5)=-F(-3)=-F(3)=F(1)=9