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Given modulus (f(a)-f(b))=1 and a not equal b, what is f(a)?

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snsett | Student, Undergraduate | (Level 1) eNoter

Posted July 22, 2012 at 1:24 PM via web

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Given modulus (f(a)-f(b))=1 and a not equal b, what is f(a)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 22, 2012 at 4:09 PM (Answer #1)

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You should assume that `b = 0`  such that:

`|f(a) - f(0)| = 1 =gt f(a) - f(0) = +- 1 =gt f(a) = f(0) +- 1`

If `f(a) = f(0) + 1`  and `f(b) = f(0) - 1` , yields:

`|f(a) - f(b)| = |f(0) + 1 -f(0)+ 1| = |2| = 2!=1`  contradiction

Hence, the function f(a) is constant and it could be either `f(a) = f(0) + 1`  or `f(a) = f(0)- 1`  such that:

`|f(a) - f(b)| = 0 != 1`  contradiction

Hence, evaluating the possible functions f(a), under given conditions, yields that there is no such a function that satisfies the given property `|f(a) - f(b)| = 1` .

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