设f(x)=(x-1)⼀(x+1),则f(x)+f(1⼀x)为___

2025-04-25 21:51:56
推荐回答(2个)
回答1:

f(x)+f(1/x)
=(x-1)/(x+1)+(1/x-1)/(1/x+1)
=(x-1)/(x+1)+((1-x)/x)/((1+x)/x)
=(x-1)/(x+1)+(1-x)/(1+x)
=(x-1+1-x)/(1+x)
=0
f(1/x)就是所在函数等式中 的x=1/x,具体例子看上面

回答2:

f(1/x)=(x-1)/(x+1)
f(x)=(1/x -1)/(1/x +1)=(1-x)/(1+x)
f(x)+f(1/x)=0