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

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 25, 2013 at 4:01 PM via web

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

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mvcdc | Student , Undergraduate | (Level 1) Associate Educator

Posted August 25, 2013 at 4:07 PM (Answer #1)

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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`

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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.`

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

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