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each of the following functions has the form f(x ) = (ax+b) mod n. assume that each function has type N base n arrow N base n, so that we can think of f as a cipher for an alphabet represented by the numbers 0, 1, ......, n -1. Use (2.6) to determine whethereach function is a bijection, and , if so, construct its inverse. Then use (2.8) to determine whether the function has fixed points (i.e., letters that dont change), and , if so find them.
b. f(x) = 2x mod 6
d. f(x) = (3x+2) mod 6
f. f(x) = (5x+3) mod 12

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