Find-f-N-N-2-f-x-f-y-x-x-N-

Question Number 156463 by MathSh last updated on 11/Oct/21

Find :

f : N^{*} \to N^{*}; 2 (f (x) + f (y)) = x

\forall x \in N^{*}

Answered by FongXD last updated on 11/Oct/21

Given : 2 (f (x) + f (y)) = x (1)

replace y with x and x with y

we get : 2 (f (y) + f (x)) = y (2)

(1) & (2), \Rightarrow x = y

substituting y = x into (1)

we get : 2 (f (x) + f (x)) = x

\Rightarrow f (x) = \frac{1}{4} x

so . \begin{matrix} f (x) = \frac{1}{4} x \end{matrix}

Commented by Rasheed.Sindhi last updated on 11/Oct/21

But f : N^{*} \to N^{*}

Here for x \in N^{*}, f (x) \in Q

I think {there}^{'} s a problem in the question .

Commented by MathSh last updated on 12/Oct/21

Yes S er

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