f(0)=0,f(1)=1,(x+y)除以2=f(x)sina+(1-sina)f(y),求a的值

导数：f(x+y)=f(x)f(y),且f'(o)=1,求f'(x)f(x+y)=f(x)f(y),且f'(o)=1,求f'(x)f(x+y)=f(x)+f(y)+2xy,且f'(o)存在,求f'(x) f(1+x)=af(x),且f'(0)=b,求f'(1) f(x+y)+f(x-y)=2f(x)f(y) 求证：f(0)=1 已知函数f(x)满足:f(1)=0,f(x)f(y)=f(x+y)+f(x-y),则f(2014)= 求具有性质f(x+y)=f(x)+f(y)/1-f(x)f(y)的函数f(x),假设f'(0)存在 f'(0)=1,f(x+y)=f(x)+f(y)+2xy,求f(x) 已知f(0)=1,f(x-y)=f(x)-y(2x-y+1),求f(x) 对于任意函数x、y,总有f(xy)-f(x)=f(y)(xy≠0）,求证1.f(1)=02.f(1/x)=-f(x)3.f(x/y)=f(x)-f(y) 若f(x+y)=f(x)+f(y),f(1)=2,则f(0)=? 高等数学f(x+y)=f(x)+f(y)/1-f(x)f(y),求f(x)f(x+y)=f(x)+f(y)/1-f(x)f(y),则f(x)=tan(ax)怎么证明?f(x)在（-∞,+∞）上有定义,且f'(x)=a(a不等于0) (0,正无穷)上f(x),f(xy)=f(x)+ f(y),x>1时f(x) f(x)定义域(0,正无穷),f(xy)=f(x)+f(y) 当x>1时,f(x) f(x+y)=f(x)*f(y)-f(x)-f(y)+2已知函数f(x)满足:对任意x,y属于R,都有f(x+y)=f(x)f(y)-f(x)-f(y)+2成立,且x>0时,f(x)>2.(1)求f(0)的值,并证明：当x f(x)对于任意正数x,y都有f(xy)=f(x)·f(y),且f(x)≠0,x>1时f(x) 已知函数f(x)满足,f(1)=1/2,f(x+y)+f(x-y)=2f(x)f(y)(x,y属于R）,则f(0)+f(1)+……+f(2013)=? f(x)定义域为R,对任意x,y属于R有f(x+y)+f(x-y)=2f(x)f(y),且f(0)不等于0求证：f(0)=1 y=f(x)为偶函数 若对一切实数x y函数f(x)都有f(x*y)=f(x)*f(y)且当x不等于y时,f(x)不等于f(y),求f(0)+f(1)的值. 函数f(x)=a^x (a>0,且a不等于1) 对于任意实数x y都有A.f(xy)=f(x)f(y)B.f(xy)=f(x)+f(y)C.f(x+y)=f(x)f(y)D.f(x+y)=f(x)+f(y) 函数f(x)=a的x次方,(a>0且a≠1),对于任意的实数x,y都有:A:f(xy)=f(x)f(y) B:f(xy)=f(x)+f(y) C:f(x+y)=f(x)f(y) D:f(x+y)=f(x)+f(y)