(2013•成都模拟)已知函数y=f(x),x∈N*,y∈N*,满足:①对任意a,b∈N*,a≠b,都有af(a)+bf(b)>af(b)+bf(a);②对任意n∈N*都有f[f(n)]=3n(II)求f(1)+f(6)+f(30);
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 19:44:40
![(2013•成都模拟)已知函数y=f(x),x∈N*,y∈N*,满足:①对任意a,b∈N*,a≠b,都有af(a)+bf(b)>af(b)+bf(a);②对任意n∈N*都有f[f(n)]=3n(II)求f(1)+f(6)+f(30);](/uploads/image/z/4027026-66-6.jpg?t=%EF%BC%882013%26%238226%3B%E6%88%90%E9%83%BD%E6%A8%A1%E6%8B%9F%EF%BC%89%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0y%3Df%EF%BC%88x%EF%BC%89%2Cx%E2%88%88N%2A%2Cy%E2%88%88N%2A%2C%E6%BB%A1%E8%B6%B3%EF%BC%9A%E2%91%A0%E5%AF%B9%E4%BB%BB%E6%84%8Fa%2Cb%E2%88%88N%2A%2Ca%E2%89%A0b%2C%E9%83%BD%E6%9C%89af%EF%BC%88a%EF%BC%89%2Bbf%EF%BC%88b%EF%BC%89%EF%BC%9Eaf%EF%BC%88b%EF%BC%89%2Bbf%EF%BC%88a%EF%BC%89%EF%BC%9B%E2%91%A1%E5%AF%B9%E4%BB%BB%E6%84%8Fn%E2%88%88N%2A%E9%83%BD%E6%9C%89f%5Bf%EF%BC%88n%EF%BC%89%5D%3D3n%EF%BC%88II%EF%BC%89%E6%B1%82f%EF%BC%881%EF%BC%89%2Bf%EF%BC%886%EF%BC%89%2Bf%EF%BC%8830%EF%BC%89%EF%BC%9B)
(2013•成都模拟)已知函数y=f(x),x∈N*,y∈N*,满足:①对任意a,b∈N*,a≠b,都有af(a)+bf(b)>af(b)+bf(a);②对任意n∈N*都有f[f(n)]=3n(II)求f(1)+f(6)+f(30);
(2013•成都模拟)已知函数y=f(x),x∈N*,y∈N*,满足:①对任意a,b∈N*,a≠b,都有af(a)+bf(b)>af(b)+bf(a);②对任意n∈N*都有f[f(n)]=3n
(II)求f(1)+f(6)+f(30);
(2013•成都模拟)已知函数y=f(x),x∈N*,y∈N*,满足:①对任意a,b∈N*,a≠b,都有af(a)+bf(b)>af(b)+bf(a);②对任意n∈N*都有f[f(n)]=3n(II)求f(1)+f(6)+f(30);
①对任意a,b∈N*,a≠b,都有af(a)+bf(b)>af(b)+bf(a)
∴(a-b)[f(a)-f(b)]>0,
∴a>b时f(a)>f(b);a