若x∈R,f(x)满足f(x*y)=f(x)+f(y),则f(x)的奇偶性

若x∈R,f(x)满足f(x*y)=f(x)+f(y),则f(x)的奇偶性 若函数f(x)满足f(x+y)=f(x)+f(y) (x,y∈R)证明f(-x)f(x) x∈R,F(x)满足F(xy)=F(x)+F(y),证明F(x)为偶函数 如何证明? x,y∈R+,满足f(xy)=f(x)+f(y),x>1时,f(x)>0,f(6)=1,求f(x+3) 若f(x)定义在R上,对任意x,y均满足f(x+y)=f(x)+f(y),试判断f(x)的奇偶性 若定义域为R函数f(x)满足f(x+y)=2*f(x)*f(y),且f(0)不等于0,证明f（x）是偶函数 f(x)满足f(1)=1/4 4f(x)f(y)=f(x+y)+f(x-y) (x ,y属于R)则 f(2010)=? 定义域在R上满足f(x+y)=f(x)+f(y)+2xy(x,y∈R),f(1)=2则f(-3)=多少 若函数y=f(x)在R上可导,且满足不等式f(x)/x 函数f(x) 满足关系f(xy)=f(x)+f(y),x,y属于R,求f(1); 函数f(x)满足关系f(xy)=f(x)*f(y)(x,y属于R）求f(1) 若函数y=f(x)满足以下条件：①对于任意的x∈R,y∈R,恒有f(x+y)=f(x)f(y);②x∈(0,+∝）时,f(x)∈(1,+∝)（1）求f(0)的值；（2）求证：f(x-y)=f(x)/f(y)（f(y)≠0）. 若函数y=f(x)满足以下条件1、对于任意的x∈R,y∈R恒有f(x+y)=f(x)f(y);2、x∈（0,∞)时,f(x)∈（0,∞)(1)求f(0)的值；（2）求证f(x-y)=f(x)/(f(y) （f(y)≠0 若奇函数y=f(x)(x属于R)满足f(2)=1,f(x+2)=f(x)+f(2)则f(5)== 定义在R上的函数f(x)总满足:f(x-y)=f(x)-f(y)(x,y∈R).且当x>0,f(x)>0,判断函数f(x)的单调性, 证明:利用f(定义在R上的函数f(x)总满足:f(x-y)=f(x)-f(y)(x,y∈R).且当x>0,f(x)>0,判断函数f(x)的单调性,证明:利用f(x) 定义在R上的函数f(x)满足f (x + y) = f (x) + f ( y )(x,y∈R),当x>0时,f (x)>0,判断f (x)在R的单调 已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?(2)证明f(x)是偶函数.请解答者列出一定的过程, 已知函数y=f(x),满足2f(x)=f(x/1)=2x,x∈R且x≠0,求f(x)