定义在非零实数集上的函数f(x)满足f(xy)=f(x)+f(y),且f(x)是区间(0,+∞)上的递增函数.(1)求f(1),f(-1)的值;(2)求证f(-x)=f(x);(3)解不等式f(2)+f(x-1/2)≤0
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![定义在非零实数集上的函数f(x)满足f(xy)=f(x)+f(y),且f(x)是区间(0,+∞)上的递增函数.(1)求f(1),f(-1)的值;(2)求证f(-x)=f(x);(3)解不等式f(2)+f(x-1/2)≤0](/uploads/image/z/3619929-57-9.jpg?t=%E5%AE%9A%E4%B9%89%E5%9C%A8%E9%9D%9E%E9%9B%B6%E5%AE%9E%E6%95%B0%E9%9B%86%E4%B8%8A%E7%9A%84%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3f%28xy%29%3Df%28x%29%2Bf%28y%29%2C%E4%B8%94f%28x%29%E6%98%AF%E5%8C%BA%E9%97%B4%280%2C%2B%E2%88%9E%29%E4%B8%8A%E7%9A%84%E9%80%92%E5%A2%9E%E5%87%BD%E6%95%B0.%EF%BC%881%EF%BC%89%E6%B1%82f%EF%BC%881%EF%BC%89%2Cf%EF%BC%88-1%EF%BC%89%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%E8%AF%81f%EF%BC%88-x%EF%BC%89%3Df%EF%BC%88x%EF%BC%89%EF%BC%9B%EF%BC%883%EF%BC%89%E8%A7%A3%E4%B8%8D%E7%AD%89%E5%BC%8Ff%EF%BC%882%EF%BC%89%2Bf%EF%BC%88x-1%2F2%EF%BC%89%E2%89%A40)
定义在非零实数集上的函数f(x)满足f(xy)=f(x)+f(y),且f(x)是区间(0,+∞)上的递增函数.(1)求f(1),f(-1)的值;(2)求证f(-x)=f(x);(3)解不等式f(2)+f(x-1/2)≤0
定义在非零实数集上的函数f(x)满足f(xy)=f(x)+f(y),且f(x)是区间(0,+∞)上的递增函数.(1)求f(1),f(-1)的值;(2)求证f(-x)=f(x);(3)解不等式f(2)+f(x-1/2)≤0
定义在非零实数集上的函数f(x)满足f(xy)=f(x)+f(y),且f(x)是区间(0,+∞)上的递增函数.(1)求f(1),f(-1)的值;(2)求证f(-x)=f(x);(3)解不等式f(2)+f(x-1/2)≤0
F(1*1)=f(1)+f(1) f(1)=0
f((-1)*(-1))=f(-1)+f(-1)
0=2f(-1)
f(-1)=0
f(-1*x)=f(-1)+f(x)
f(-x)=f(x)
f(2)+f(x-1/2)≤0
f(2*(x-1/2))≤0
f(2x-1)≤0
因为f(-x)=f(x)
所以是奇函数
所以0