Question

f(x)的反函数f^-1=log2(1+x)/(1-x),求f(x)的解析式和解不等式1-f(x)>1/(4^x-1)

Answer 1

由原式得

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

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

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

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

x=1-1/2^y+1

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