函数f(x)的定义域为D={x x∈且x≠0},且满足对于任意的x1,x2∈D,有f(x1×x2)=f(x1)+f(x2).(1)求f(1)及f(-1)的值(2)判断f(x)的奇偶性并证明
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/19 04:58:38
![函数f(x)的定义域为D={x x∈且x≠0},且满足对于任意的x1,x2∈D,有f(x1×x2)=f(x1)+f(x2).(1)求f(1)及f(-1)的值(2)判断f(x)的奇偶性并证明](/uploads/image/z/2796043-67-3.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BAD%3D%7Bx+x%E2%88%88%E4%B8%94x%E2%89%A00%7D%2C%E4%B8%94%E6%BB%A1%E8%B6%B3%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%9A%84x1%2Cx2%E2%88%88D%2C%E6%9C%89f%28x1%C3%97x2%29%3Df%28x1%29%2Bf%28x2%29.%281%29%E6%B1%82f%281%29%E5%8F%8Af%EF%BC%88-1%EF%BC%89%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E5%88%A4%E6%96%ADf%EF%BC%88x%EF%BC%89%E7%9A%84%E5%A5%87%E5%81%B6%E6%80%A7%E5%B9%B6%E8%AF%81%E6%98%8E)
xՑN0_cƤgEXBH)Ԙ]RTZ1AAHQӄ7lӭSVrGilo9i)1ۧ)Lbٕ'UŅZi ūf94U#hS
<}8 Hoәf6(kԏt0|3
函数f(x)的定义域为D={x x∈且x≠0},且满足对于任意的x1,x2∈D,有f(x1×x2)=f(x1)+f(x2).(1)求f(1)及f(-1)的值(2)判断f(x)的奇偶性并证明
函数f(x)的定义域为D={x x∈且x≠0},且满足对于任意的x1,x2∈D,有f(x1×x2)=f(x1)+f(x2).
(1)求f(1)及f(-1)的值
(2)判断f(x)的奇偶性并证明
函数f(x)的定义域为D={x x∈且x≠0},且满足对于任意的x1,x2∈D,有f(x1×x2)=f(x1)+f(x2).(1)求f(1)及f(-1)的值(2)判断f(x)的奇偶性并证明
1 1) 令x1=x2=1
f(x1×x2)=f(x1)+f(x2).
f(1)=f(1)+f(1) f(1)=0
2)令 x1=x2=-1
f(x1×x2)=f(x1)+f(x2).
f(1)=f(-1)+f(-1) f(-1)=0
2 令 x1=-1 f(-x2)=f(-1)+f(x2)=f(x2) 所以f(x)为偶函数