A function `y = log_12 x` would be the inverse function of what exponential function?



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Posted on (Answer #1)

In order to get the inverse of the function `f(x)` which we denote as `f^(-1)(x)`, we simply interchange x and y, and then solve for y:

`y = log_12 x`

Interchanging x and y:

`x = log_12 y`  

To solve for y, we note that:

`y = log_a b` is equivalent to `a^y = b` , using definitions of log and exponents.

Hence, we can solve for y` `as:

`y = 12^x`

This means that:

`f^(-1)(x) = 12^x`


To check, note that `f(f^(-1)(x)) = f^(-1)(f(x)) = x`

`f^(-1)(f(x)) = 12^(log_12 x) = x` also,

`f(f^(-1)x)) = log_12 (12^x) = x.`


The inverse function of the function f(x) = log(base 12)x is f^-1(x) = 12^x.


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