ANSWER
[tex]f^{-1}(x)\text{ = }\frac{6x\text{ + 1}}{5}[/tex]EXPLANATION
We want to find the inverse:
[tex]f(x\text{) = }\frac{5x\text{ - 1}}{6}[/tex]First, change f(x) to y:
[tex]y\text{ = }\frac{5x\text{ - 1}}{6}[/tex]Now, make x the subject of formula:
[tex]\begin{gathered} 6y\text{ = 5x - 1} \\ 6y\text{ + 1 = 5x} \\ x\text{ = }\frac{6y\text{ + 1}}{5} \end{gathered}[/tex]Now, change x to f-1(x), change y to x:
[tex]f^{-1}(x)\text{ = }\frac{6x\text{ + 1}}{5}[/tex]That is the inverse.
