Question

Hello I’m doing this assignment and got stuck on this question

Answer 1

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:

`\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)=(\log x)/(\log b)=\log_xb \end{gathered}`

Therefore the correct option is D.