In order to find the inverse function, we need to switch the function f(x) by x and then the variable x by the inverse function f^-1(x). Then, we solve for the inverse function
So, for the function f(x), we have:
[tex]\begin{gathered} f(x)=3x+5\\ \\ x=3f^{-1}(x)+5\\ \\ 3f^{-1}(x)=x-5\\ \\ f^{-1}(x)=\frac{1}{3}x-\frac{5}{3} \end{gathered}[/tex]
Therefore the correct option is C.
