Question

which function is the inverse of $f(x)=\log_{3}x$? (5 points)○ $f^{-1}(x)=3^{\log x}$○ $f^{-1}(x)=3^{x}$○ $f^{-1}(x)=3x$○ $f^{-1}(x)=x^{3}$

Explanation:

Step1: Set $y = f(x)$

Let $y = \log_{3} x$

Step2: Rewrite in exponential form

By logarithm definition, $x = 3^y$

Step3: Swap $x$ and $y$

To find inverse, swap variables: $y = 3^x$

Step4: Define inverse function

This gives $f^{-1}(x) = 3^x$

Answer:

$\boldsymbol{f^{-1}(x) = 3^x}$ (the second option)