设函数y=f(x)的定义域是正实数集,且有f(xy)=f(x)+f(y),又知f(8)=3,则f(根号2)=?
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![设函数y=f(x)的定义域是正实数集,且有f(xy)=f(x)+f(y),又知f(8)=3,则f(根号2)=?](/uploads/image/z/2569325-5-5.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E6%98%AF%E6%AD%A3%E5%AE%9E%E6%95%B0%E9%9B%86%2C%E4%B8%94%E6%9C%89f%28xy%29%3Df%28x%29%2Bf%28y%29%2C%E5%8F%88%E7%9F%A5f%288%29%3D3%2C%E5%88%99f%28%E6%A0%B9%E5%8F%B72%29%3D%3F)
设函数y=f(x)的定义域是正实数集,且有f(xy)=f(x)+f(y),又知f(8)=3,则f(根号2)=?
设函数y=f(x)的定义域是正实数集,且有f(xy)=f(x)+f(y),又知f(8)=3,则f(根号2)=?
设函数y=f(x)的定义域是正实数集,且有f(xy)=f(x)+f(y),又知f(8)=3,则f(根号2)=?
f(2)=f(√2)+f(√2)=2f(√2)
f(4)=f(2)+f(2)=2f(2)
f(8)=f(2)+f(4)=3f(2)=6f(√2)
∴f(√2)=1/6×3=1/2
f(8)=f(2*4)=f(2)+f(4)
=f((√2*(√2)+f(2*2)
=f((√2)+f((√2)+f(2)+f(2)
=f((√2)+f((√2)+f((√2)+f((√2)+f((√2)+f((√2)
=6f((√2)=3,所以f((√2)=3/6=1/2