Answer:
[tex]f^{-1} (2)=\frac{5}{3}[/tex]
Step-by-step explanation:
To find the inverse of a function, we must replace y for x and then solve for y.
[tex]y=\frac{3x-1}{2} \\x=\frac{3y-1}{2} \\2x=3y-1\\3y=2x+1\\y=\frac{2x+1}{3} \\f^{-1} (x)=\frac{2x+1}{3}[/tex]
Now we can substitute x=2 into our inverse function
[tex]f^{-1} (2)=\frac{2(2)+1}{3} \\f^{-1} (2)=\frac{5}{3}[/tex]
