设函数f(x)的定义域在正实数集上,若对任意x1>0,x2>0均有f(x1+x2)=f(x1)+f(x2)且f(8)=3,求f(2).
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![设函数f(x)的定义域在正实数集上,若对任意x1>0,x2>0均有f(x1+x2)=f(x1)+f(x2)且f(8)=3,求f(2).](/uploads/image/z/1324689-33-9.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E5%9C%A8%E6%AD%A3%E5%AE%9E%E6%95%B0%E9%9B%86%E4%B8%8A%2C%E8%8B%A5%E5%AF%B9%E4%BB%BB%E6%84%8Fx1%EF%BC%9E0%2Cx2%EF%BC%9E0%E5%9D%87%E6%9C%89f%28x1%2Bx2%29%3Df%28x1%29%2Bf%28x2%29%E4%B8%94f%288%29%3D3%2C%E6%B1%82f%282%29.)
设函数f(x)的定义域在正实数集上,若对任意x1>0,x2>0均有f(x1+x2)=f(x1)+f(x2)且f(8)=3,求f(2).
设函数f(x)的定义域在正实数集上,若对任意x1>0,x2>0均有f(x1+x2)=f(x1)+f(x2)且f(8)=3,求f(2).
设函数f(x)的定义域在正实数集上,若对任意x1>0,x2>0均有f(x1+x2)=f(x1)+f(x2)且f(8)=3,求f(2).
F(8)=F(2+6)=F(2)+F(6)
=F(2)+F(2+4)
=F(2)+F(2)+F(4)
=F(2)+F(2)+F(2)+F(2)
=4F(2)
因此F(2)=3/4