What is the inverse of f(x) = 2^x ?

1 Answer
Dec 23, 2015

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

Explanation:

color(white)(xx)f(x)=2^x

=>y=color(red)2^xcolor(white)(xxxxxxxxxxx) (base is color(red)2)
=>x=log_color(red)2 ycolor(white)(xxxxxxxxxxx)(logarithm definition)

=>f^-1(x)=log_2 x

In RR^2, f^-1(x) graph have to be symmetrical of f(x) graph:
http://rechneronline.de/http://rechneronline.de/
y=f(x), y=x, and y=f^-1(x) graphs