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Sonia Ayers

Sonia Ayers

Answered question

2022-07-07

Let f : R R be a function such that for any irrational number r, and any real number x we have f ( x ) = f ( x + r ). Show that f is a constant function.

Answer & Explanation

amanhantmk

amanhantmk

Beginner2022-07-08Added 17 answers

Let x , y R . Choose irrational r such that x + r , y + r are irrational. Then we have
f ( x ) = f ( x + y + r ) = f ( y + x + r ) = f ( y )
Thus f is constant.

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