Explanation:
The equation is given below as
[tex]f^{-1}(x)=\frac{6}{5}(x)-9[/tex]
Concept:
make x, the subject of the formula
[tex]\begin{gathered} f^{-1}(x)=\frac{6}{5}(x)-9 \\ y=\frac{6}{5}(x)-9 \\ y+9=\frac{6}{5}x \\ multiply\text{ through by 5} \\ 5y+45=6x \\ divide\text{ through by 6, we will have} \\ \frac{5y}{6}+\frac{45}{6}=\frac{6x}{6} \\ x=\frac{5}{6}(x+9) \end{gathered}[/tex]
Hence,
The final answer is
[tex]f(x)=\frac{5}{6}(x+9)[/tex]
The FIRST OPTION is the correct answer
