To show that j(x) and k(x) are inverse functions, we show that the following condition holds.
[tex]j(k(x))=k(j(x))=x[/tex][tex]j(k(x))=11.6e^{ln(\frac{x}{11.6})}=11.6\times\frac{x}{11.6}=x[/tex]Similarly:
[tex]\begin{gathered} k(j(x))=\ln (\frac{11.6e^x}{11.6}) \\ =\ln e^x=x \end{gathered}[/tex]Therefore, they are inverses.