f(x) = 8(x -3) (option C)
Explanation:
[tex]f^{-1}(x)\text{ = }\frac{x}{8}+3[/tex]let y = inverse of f(x)
[tex]y\text{ = }\frac{x}{8}+\text{ 3}[/tex]Interchange x and y:
[tex]\begin{gathered} x=\text{ }\frac{y}{8}+\text{ 3} \\ mu\text{ltiply through by 8:} \\ 8(x)\text{ = 8}(\frac{y}{8})+\text{ 3(8)} \\ 8x\text{ = y + 24} \end{gathered}[/tex][tex]\begin{gathered} \text{make y the suject of by subtracting 24 to both sides} \\ 8x\text{ - 24 = y} \\ y\text{ = 8(x - 3) (option C)} \\ f(x)\text{ = 8(x - 3) (option C)} \end{gathered}[/tex]