Answer : [tex]\bf \dfrac{x+1}{3}[/tex]
A function is given to us and we need to find out the inverse of the function . The given function is ,
[tex]\rm \implies f(x) = 3x - 1 [/tex]
Step 1: Substitute y = f(x) :-
[tex]\rm \implies y = 3x -1[/tex]
Step 2: Interchange x and y :-
[tex]\rm \implies x = 3y - 1[/tex]
Step 3: Solve for y :-
[tex]\rm \implies 3y = x + 1 \\[/tex]
[tex]\rm \implies y =\dfrac{x+1}{3} [/tex]
Step 4: Replace y with f-¹(x) :-
[tex]\rm \implies \underline{\boxed{\red{\rm f^{-1}(x) = \dfrac{x+1}{3}}}} [/tex]
Hence the inverse of the function is (x+1)/3.
I hope this helps .
