If fx+y2=f(x)+f(y)2 for all real x and y and f1(0) exists and equals to -1 and f(0)=1 , then f1(x)=

fx+y2=fx+fy2....1Put y=0, f(0)=1fx2=12fx+1⇒fx=2fx2−1→2f'x=lth→0fx+h−fxh=lth→0f2x+2h2−fxh=lth→0f2x+f2h2−fxh=lth→0f2x+f2h−2fx2h=lth→02fx−1+f2h−2fx2h=lth→0f2h−12h=f'0f'x=−1