In order to calculate the inverse function, we need to switch x by f^-1(y) and f(x) by x, then we solve for f^-1(y).
So we have:
[tex]\begin{gathered} F(x)=b^x=y\\ \\ x=b^{F-1}\\ \\ \log x=\log b^{F-1}\\ \\ \log x=F^{-1}(y)\log b\\ \\ F^{-1}(y)=\frac{\log x}{\log b}=\log_xb \end{gathered}[/tex]
Therefore the correct option is D.
