Question

已知f（x）的反函数f-1(x)=log2(1+x/1-x),求f(x)的解析式

Answer 1

就是求y=f-1(x)反函数
2^y=(1+x)/(1-x)=-(x-1+2)/(x-1)
=-1-2/(x-1)
2/(x-1)=-2^y-1
x-1=-2/(2^y+1)
x=1-2/(2^y-1)=(2^y-1)/(2^y+1)
所以f(x)=(2^x-1)/(2^x+1)

Answer 2

令a=x²+y²
(a+1)(a-3)=5
a²-2a-3-5=0
a²-2a-8=0
(a-4)(a+2)=0
a=4,a=-2
a=x²+y²≥0
所以x²+y²=4