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## Homework Statement

Let S be the subset of the integers {0, 1, 2, 3, 4, 5, 6}, and let f be the function from S to S defined by f(x) = (4x+3) mod 7. Find a formula for f<superscript>-1 (the inverse of f, I don't know how to type that).

## Homework Equations

I know that the mod function is defined by floor function (a - n floor(n\a). But I'm still unable to create an inverse function with one inverse function for all values. I made a piecewise function that works for those values, but I feel like there should be a better method. Does anybody know an inverse rule for either floor or modulus?

## The Attempt at a Solution

f(x) = {2x+1, 0 <= x <= 2}

{2x-6, 3 <= x <= 6}