求y=(5^x+1)/(2+5x)的反函数,

题目

求y=(5^x+1)/(2+5x)的反函数,

答案

令a=5^x
y=(a+1)/(2+a)
2y+ay=a+1
ay-a=1-2y
a(y-1)=1-2y
所以a=5^x=(1-2y)/(y-1)
x=log5[(1-2y)/(y-1)]
所以反函数是y=log5[(1-2x)/(x-1)]