Question

求下列函数的反函数 y=(1-x)/(1+x) y=(ax+b)/(cx+d) (db-cb≠0)

Answer 1

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

y(1+x)=1-x

(y+1)x=1-y

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

将x、y互换

反函数为y=(1-x)/(x+1) (x≠-1)

y=(ax+b)/(cx+d)

cyx+dy=ax+b

(cy-a)x=b-dy

x=(b-dy)/(cy-a)

将x、y互换

反函数为y=(b-dx)/(cx-a) (x≠a/c)

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

y·2^x +y=2^x

(1-y)·2^x=y

2^x=y/(1-y)

x=log2[y/(1-y)]

y/(1-y)>0 y/(y-1)