Logic Function Mod5 Problem

I am looking for a solution:

A= {0,1,2,3,4};

F(x) = 3x - 1 (mod5)

Could you help me to find the inverse. I am struggling with this as it seems to be not to be onto or 1to1.

Thank开发者_StackOverflow社区 you for your help.

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x = 2y + 2, where y = F(x)

-> 3x - 1 = 3(2y+2) - 1 = 6y + 5 = y (mod 5)

edit: if you want this to be evaluated for the list of principal values mod 5 [0,1,2,3,4], just evaluate 2y+2 for each of these, and what you get is [2,4,1,3,0]. Which, if you plug back into 3x-1, you get [0,1,2,3,4] as expected.