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1. Dec 10, 2011

### mtayab1994

1. The problem statement, all variables and given/known data

$$f\left(x^{2}+f(y)\right)=y-x^{2}$$

2. Relevant equations

Find all functions f that satisfy the relationship for every real x and y.

3. The attempt at a solution

is this correct reasoning?

for x=0: $$f(y)=f^{-1}(y)$$

for x>0: $\existsxεℝ$: $$x=k^{2}$$

$$f(k^{2}+f(0))=-k^{2}+f(0)$$

for x<0 $\existsxεℝ$: $$x=-k^{2}$$

$$f(0)=f(k^{2}+f(-k^{2}))$$ = $$f(-k^{2})-k^{2}$$ which entails:

$$f(-k^{2})=f(0)+k^{2}$$ =$$-(-k^{2})+f(0)$$

2. Dec 10, 2011

### SammyS

Staff Emeritus
This question has been previously discussed.

http:

Is there anything new in what you're posting this time?

3. Dec 10, 2011

### mtayab1994

yes for x>0 and for x<0 i want to know if what i did is correct.

4. Dec 10, 2011

### micromass

Staff Emeritus