Solution
Step 1
Write the inverse function:
[tex]f^{-1}(x)\text{ = }\frac{6}{5}x\text{ - 9}[/tex]
Step 2
[tex]\begin{gathered} Let\text{ f}^{-1}(x)\text{ = y} \\ \\ y\text{ = }\frac{6}{5}x\text{ - 9} \\ \\ Make\text{ x the subject of the formula} \\ \\ y\text{ + 9 = }\frac{6}{5}x \\ \\ Divide\text{ both sides by }\frac{6}{5} \\ \\ x\text{ = }\frac{5}{6}(y\text{ + 9\rparen} \\ \\ f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen} \end{gathered}[/tex]
Final answer
[tex]f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen}[/tex]
