f(x)=?

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Thamim Zahin
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f(x)=?

Unread post by Thamim Zahin » Tue Mar 21, 2017 9:26 pm

Find all functions $f:Q \rightarrow Q$ such that
\[f(1)=2\]
and
\[f(xy)=f(x)f(y)−f(x+y)+1\]
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Zawadx
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Re: f(x)=?

Unread post by Zawadx » Thu Mar 23, 2017 12:27 am

This can be solved by the basic arguments used to solve Cauchy's FE over Q. Try it yourself!

Hint if you're extremely desperate:
$$ f( n + \frac{1}{m}) = n + f( \frac{1}{m} ) $$
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