已知函數(shù)f(x)=log2(x+1/x-1)
求f(x)的反函數(shù)f^-1(x),并求使得函數(shù)g(x)=f^-1(x)-log2(k)有零點(diǎn)的實(shí)數(shù)k是取值范圍
解析：∵函數(shù)f(x)=log[2,(x+1)/(x-1)]
y=log[2,(x+1)/(x-1)]
2^y=(x+1)/(x-1)
x=(2^y+1)/(2^y-1)
y=(2^x+1)/(2^x-1)
f(x)的反函數(shù)f^-1(x)=(2^x+1)/(2^x-1)


當(dāng)x→-∞時(shí),f^-1(x)→-1；當(dāng)x→+∞時(shí),f^-1(x)→1；
使得函數(shù)g(x)=f^-1(x)-log2(k)有零點(diǎn)
須使|log(2,k)|>1==>log(2,k)0k>2
∴0