Question

Which statement identifies how to show that j(x) = 11.6e^x and k(x) = In (x/11.6) are inverse functions?

Answer 1

To show that j(x) and k(x) are inverse functions, we show that the following condition holds.

`j(k(x))=k(j(x))=x`
`j(k(x))=11.6e^{ln((x)/(11.6))}=11.6*(x)/(11.6)=x`

Similarly:

`\begin{gathered} k(j(x))=\ln ((11.6e^x)/(11.6)) \\ =\ln e^x=x \end{gathered}`

Therefore, they are inverses.