Step 1:
Write the function
[tex]\text{y = - }\log ^{(x-1)}_{}\text{ + 2}[/tex]Step 2:
To find the inverse of the function, make x subject of the formula
[tex]\begin{gathered} y\text{ = - }\log ^{(x-1)}_{}+\text{ 2} \\ \log ^{(x-1)}_{}\text{ = 2 - y} \\ x-1\text{ = }10^{(2-y)} \\ x=10^{(2-y)}\text{ + 1} \\ y^{-1}(x)=10^{(2-x)}\text{ + 1} \end{gathered}[/tex][tex]\begin{gathered} Or \\ y^{-1}(x)\text{ = ln(2-x) + 1} \end{gathered}[/tex]