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

1 Answer
Özgür Özer
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)#

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