Finding a valuating and interpreting an inverse function for given linear relationship

Given:
[tex]P(n)=0.8n+5.2[/tex](b)
[tex]\begin{gathered} x=0.8P^{\mleft\{-1\mright\}}\mleft(x\mright)+5.2 \\ 0.8P^{\mleft\{-1\mright\}}\mleft(x\mright)=x-5.2 \\ P^{\mleft\{-1\mright\}}\mleft(x\mright)=\frac{x-5.2}{0.8} \end{gathered}[/tex](c)
[tex]\begin{gathered} P^{\mleft\{-1\mright\}}\mleft(10.4\mright)=\frac{10.4-5.2}{0.8} \\ =\frac{5.2}{0.8} \\ =6.5 \end{gathered}[/tex]