Question

Let f : R → R⁺ be defined by f(x) = a^x, a > 0 and a ≠ 1. Write f⁻¹ (x).

Answer 1

$$\begin{gathered} \text{Let}{f}^{-1}\left(x\right)=y...\left(1\right) \\ \Rightarrow f\left(y\right)=x \\ \Rightarrow a^y=x \\ \Rightarrow y={\log }_{a}x \\ \Rightarrow f^{-1}\left(x\right)=\log {}_{a}x[\text{from}\left(1\right)\text{]} \end{gathered}$$