Question

Consider the logarithmic function f(x)=log12 x.


Determine an expression for g(x),
the inverse function of f(x).

Answer 1

To find the inverse of the function \( f(x) = \log_{12}(x) \), we will follow these steps:

1. Replace \( f(x) \) with \( y \):
\[
y = \log_{12}(x)
\]

2. Rewrite the logarithmic equation in exponential form. The definition of the logarithm tells us that if \( y = \log_{12}(x) \), then:
\[
x = 12^y
\]

3. Solve for \( x \) in terms of \( y \):
\[
x = 12^y
\]

4. Now, swap \( x \) and \( y \) to find the inverse function \( g(x) \):
\[
y = 12^x
\]

Hence, the inverse function \( g(x) \) is given by:
\[
g(x) = 12^x
\]