Given: A function
[tex]f(x)=3x+1[/tex]Required: To find the inverse of the given function.
Explanation: We will use the concept of inverse functions to find out the inverse of f(x). Let
[tex]\begin{gathered} f(x)=y \\ y=3x+1 \end{gathered}[/tex]Interchange x and y,
[tex]x=3y+1[/tex]Now express y in terms of x as follows
[tex]y=\frac{x-1}{3}[/tex]From the definition of an inverse function,
[tex]f(x)=y\Rightarrow x=f^{-1}(y)[/tex]Therefore,
[tex]f^{-1}(y)=\frac{x-1}{3}[/tex]Thus the inverse of y=3x+1 is
[tex]f^{-1}(x)=\frac{x-1}{3}[/tex]Final Answer:
[tex]f^{-1}(x)=\frac{x-1}{3}[/tex]