Question

设f（xx-1）=logxx/xx-2且f（g（x））=logx,求g（x）

Answer 1

f（xx-1）=logxx/xx-2

请问你这xx是啥意思?

x的平方?

后面的logxx/xx-2是log（x^2/(x^2-2))?

令y=x^2/(x^2-2) 则

x^2=2y/(y-1)

x^2-1=(y+1)/(y-1)

所以 f((y+1)/(y-1))=log(y)

g(y)=(y+1)/(y-1)

即g(x)=(x+1)/(x-1)