For a positive integer x, let f(x) be the remainder obtained by dividing x by 3. For
Chapter 10, Problem 113(choose chapter or problem)
For a positive integer x, let f(x) be the remainder obtained by dividing x by 3. For example, f(6) = 0, because 6 divided by 3 equals 2 with a remainder of 0. Likewise, f(7) = 1, because 7 divided by 3 equals 2 with a remainder of 1. (a) Evaluate f(8), f(17), f(29), f(99). (b) Find a formula for f(3x). (c) Is f(x) invertible? (d) Find a formula in terms of f(x) for f(f(x)). (e) Does f(x + y) necessarily equal f(x) + f(y)?
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