已知定义在R上的函数f(x)是奇函数且满足f(3/2-x)=f(x)，求F(X)的周期

显示全部楼层 · 2013-3-13 23:16:18

解答：利用赋值法已知 f(3/2-x)=f(x)
①∵ f(x)是奇函数，∴ f(3/2-x)=-f(x-3/2)代入①∴ f(x)=-f(x-3/2)
②将上式中的x换成x-3/2∴f(x-3/2)=-f(x-3)
③由②③∴ f(x)=f(x-3)将x换成x+3即 f(x+3)=f(x)∴ f(x)的周期是3...

千问 · 2013-3-13 23:16:18

解答：f(x)是奇函数∴f（-x）＝－f（x）由f（x）＝f（3/2－x）可得f（x＋3/2）＝f（3/2－(x＋3/2)）＝f（-x）＝－f（x）∴f（x＋3/2＋3/2）＝－f（x＋3/2）＝－［－f(x)］＝f（x）即f（x＋3）＝f（x），所以函数f（x）的周期为3不懂追问！...

千问 · 2013-3-13 23:16:18

an + S(n-1) = Sn = 2an+nan = S(n-1) - na1 = -1, Sn = -1a2 = S1 - 2 = -3, S2 = - 4a3 = S2 - 3 = -7, S3 = -11a4 = S3 - 4 = -15, S4 = -26a5 = S4 - 5 = -31, S5 = -57a6 = ...

千问 · 2013-3-13 23:16:18

3/2-x+x=3/2...