Question

If f : R⁺ → R is defined as f(x) = log₃ x, then f^–1(x) = ______________.

Answer 1

Given: f(x) = log₃x

$$\begin{gathered} f\left(x\right)={\log }_{3}x \\ \Rightarrow y={\log }_{3}x \\ \Rightarrow x=3^y \\ \mathrm{Thus},f^{-1}\left(y\right)=3^y. \end{gathered}$$

Hence, f⁻¹(x) = 3^x.