Suppose that E is an alphabet, and that f :E* → E* has the property that f(ơ) = o for every o e E an f(xy) = f(x) f(y) for every x, y € £*. Prove that for every x € E*, f (x) = x.

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A: The answer provided below has been developed in a clear step by step manner.

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A: Suppose   is convex. We have to show that:

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A: g(m, n) = g(m-1, n) + 2n             = g(m-2, n) + 2n + 2n            = g(m-3, n) + 2n + 2n + 2n…

Q: Kailash ben

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A: f(x) = (3x+11) (mod 11) X = {0, 1, 2, ..., 25} GCD(3,26)=1

Q: 6. Is the function h: Z → Z defined by ( 2n if n 20 h(n) -n if n < 0 one-to-one? Is it onto?

A: The solution is given as follows

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