How do you find the inverse of f(x)=2^(x+1) -2?

1 Answer
Dec 16, 2015

color(white)(xx)f^-1(x)=log_2 ((x+2)/2)

Explanation:

color(white)(xx)f(x)=2^(x+1)-2

=>y=2^(x+1)-2
=>ycolor(red)(+2)=2^(x+1)-2color(red)(+2)

=>2^(x+1)=y+2
=>x+1=log_2 (y+2)
=>x+1color(red)(-1)=log_2 (y+2)color(red)(-1)

=>x=log_2 (y+2)-1
=>x=log_2 ((y+2)/2)

=>f^-1(x)=log_2 ((x+2)/2)