设函数y=f(x)对任意非零实数x1,x2满足f(x1x2)=f(x1)+f(x2)(1)证明f(1)=f(-1)=0(2)证明f(x)是偶函数(3)已知f(x)为(0,+无穷)上的增函数,且满足f(x)+f(x-1\2)≤0,求x
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设函数y=f(x)对任意非零实数x1,x2满足f(x1x2)=f(x1)+f(x2)(1)证明f(1)=f(-1)=0(2)证明f(x)是偶函数(3)已知f(x)为(0,+无穷)上的增函数,且满足f(x)+f(x-1\2)≤0,求x
设函数y=f(x)对任意非零实数x1,x2满足f(x1x2)=f(x1)+f(x2)
(1)证明f(1)=f(-1)=0
(2)证明f(x)是偶函数
(3)已知f(x)为(0,+无穷)上的增函数,且满足f(x)+f(x-1\2)≤0,求x
设函数y=f(x)对任意非零实数x1,x2满足f(x1x2)=f(x1)+f(x2)(1)证明f(1)=f(-1)=0(2)证明f(x)是偶函数(3)已知f(x)为(0,+无穷)上的增函数,且满足f(x)+f(x-1\2)≤0,求x
1)
f(1)=f(1)+f(1)=2f(1)
f(1)=0
f(1)=f(-1)+f(-1)=2f(-1)=0
f(-1)=0
2)
f(-x)=f(x)+f(-1)=f(x)
所以:f(x)是偶函数
3)
f(x)+f(x-1\2)=f(x+x-1/2)=f(2x-1/2)