Question

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

Answer 1

`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:

`y=f(x)`, `y=x`, and `y=f^-1(x)` graphs