):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)...):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)=1/(x-1),求f(x),g(x).
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/10 17:47:44
![):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)...):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)=1/(x-1),求f(x),g(x).](/uploads/image/z/6462673-25-3.jpg?t=%29%EF%BC%9A%E5%87%BD%E6%95%B0f%28x%29%2Cg%28x%29%E9%83%BD%E5%AE%9A%E4%B9%89%E5%9C%A8%28%E8%B4%9F%E6%97%A0%E7%A9%B7%E5%A4%A7%2C-1%29U%28-1%2C1%29U%281%2C%E6%AD%A3%E6%97%A0%E7%A9%B7%E5%A4%A7%29%E4%B8%8A%2Cf%28x%29...%29%EF%BC%9A%E5%87%BD%E6%95%B0f%28x%29%2Cg%28x%29%E9%83%BD%E5%AE%9A%E4%B9%89%E5%9C%A8%28%E8%B4%9F%E6%97%A0%E7%A9%B7%E5%A4%A7%2C-1%29U%28-1%2C1%29U%281%2C%E6%AD%A3%E6%97%A0%E7%A9%B7%E5%A4%A7%29%E4%B8%8A%2Cf%28x%29%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0%2Cg%28x%29%E6%98%AF%E5%A5%87%E5%87%BD%E6%95%B0%2C%E4%B8%94f%28x%29%2Bg%28x%29%3D1%2F%28x-1%29%2C%E6%B1%82f%28x%29%2Cg%28x%29.)
):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)...):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)=1/(x-1),求f(x),g(x).
):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)...
):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)=1/(x-1),求f(x),g(x).
):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)...):函数f(x),g(x)都定义在(负无穷大,-1)U(-1,1)U(1,正无穷大)上,f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)=1/(x-1),求f(x),g(x).
f(-x)=f(x)
g(-x)=-g(x)
令h(x)=f(x)+g(x)=1/(x-1) (1)
h(-x)=f(-x)+g(-x)=f(x)-g(x)=1/(-x-1)=-1/(x+1) (2)
(1)+(2)
2f(x)=2/(x²-1)
f(x)=1/(x²-1)
g(x)=h(x)-f(x)=x/(x²-1)
f(x)+g(x)=1/(x-1) (1)
f(-x)+g(-x)=f(x)-g(x)=1/(-x-1) (2)
(1)-(2)得2g(x)=2x/(x^2-1)
所以
g(x)=x/(x^2-1)
f(x)=1/(x-1)-x/(x^2-1)=1/(x^2-1)
依题f(x)+g(x)=1/(X-1),将-x代入根据奇偶性得
f(x)-g(x)=1/(-x-1),联立,解之得f(x)=1/(x^2-1),
g(x)=x/(x^2-1),最后记得说下定义域