作业帮已知函数f(x)=log2(1+x/1-x),求证f(x1)+f(x2)=f[(x1+x2)/(1+x1x2)
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已知函数f(x)=log2(1+x/1-x),求证f(x1)+f(x2)=f[(x1+x2)/(1+x1x2)
已知函数f(x)=log2(1+x/1-x),求证f(x1)+f(x2)=f[(x1+x2)/(1+x1x2)
已知函数f(x)=log2(1+x/1-x),求证f(x1)+f(x2)=f[(x1+x2)/(1+x1x2)
f(x1)+f(x2)=log2[(1+x1)/(1-x1)]+log2[(1+x2)/(1-x2)]
=log2[(1+x1)(1+x2)/(1-x1)(1-x2)]
f[(x1+x2)/(1+x1x2)]
=log2[1+(x1+x2)/(1+x1x2)]/[1-(x1+x2)/(1+x1x2)]
就是要证明(1+x1)(1+x2)/(1-x1)(1-x2)=[1+(x1+x2)/(1+x1x2)]/[1-(x1+x2)/(1+x1x2)
1+(x1+x2)/(1+x1x2)]/[1-(x1+x2)/(1+x1x2)
=(x1x2+x1+x2)/(x1x2-x1-x2)
而(1+x1)(1+x2)/(1-x1)(1-x2)
=(1+x1x2+x1+x2)/(1+x1x2-x1-x2)
显然这个等式不成立,所以题目有错.
f(x1)+f(x2)=log2(1+x1/(1-x1))+log2(1+x2/(1-x2))
=log2[1+x1/(1-x1)+x2/(1-x2)+x1x2/(1-x1)(1-x2)]
=log2[1+(x1-x1x2+x2-x1x2)/(1-x1)(1-x2)+x1x2/(1-x1)(1-x2)]
f[(x1+x2)/(1+x1x2)]
=log2[1+((x...
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f(x1)+f(x2)=log2(1+x1/(1-x1))+log2(1+x2/(1-x2))
=log2[1+x1/(1-x1)+x2/(1-x2)+x1x2/(1-x1)(1-x2)]
=log2[1+(x1-x1x2+x2-x1x2)/(1-x1)(1-x2)+x1x2/(1-x1)(1-x2)]
f[(x1+x2)/(1+x1x2)]
=log2[1+((x1+x2)/(1+x1x2))/((1-(x1+x2)/(1+x1x2))]
=log2[1+(x1+x2)/(1-x1-x2+x1x2)]
……思路大致如上，可是俺怎么得不到这个结论？楼主没把题目写错吧？辛苦楼主看看我的过程是不是有啥错误，这样应该能出的来~
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