Answer: Choice D. [tex]f^{-1}(x) = \frac{6x+2}{3}[/tex]
Work Shown:
The idea is that you replace f(x) with y, swap x and y, then solve for y to get the inverse.
[tex]f(x) = \frac{3x-2}{6}\\\\y = \frac{3x-2}{6}\\\\x = \frac{3y-2}{6}\\\\6x = 3y-2\\\\3y-2 = 6x\\\\3y = 6x+2\\\\y = \frac{6x+2}{3}\\\\f^{-1}(x) = \frac{6x+2}{3}\\\\[/tex]
