设函数f(x)=(ax²+1)÷(bx+c)是奇函数(a,b,c∈Z),且f(1)=2,f (2)<3.(1) 求a,b,c的值.
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![设函数f(x)=(ax²+1)÷(bx+c)是奇函数(a,b,c∈Z),且f(1)=2,f (2)<3.(1) 求a,b,c的值.](/uploads/image/z/1331931-3-1.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%EF%BC%88ax%26%23178%3B%EF%BC%8B1%EF%BC%89%C3%B7%EF%BC%88bx%2Bc%EF%BC%89%E6%98%AF%E5%A5%87%E5%87%BD%E6%95%B0%EF%BC%88a%2Cb%2Cc%E2%88%88Z%29%2C%E4%B8%94f%EF%BC%881%29%3D2%2Cf+%282%29%EF%BC%9C3.%281%29+%E6%B1%82a%2Cb%2Cc%E7%9A%84%E5%80%BC.)
设函数f(x)=(ax²+1)÷(bx+c)是奇函数(a,b,c∈Z),且f(1)=2,f (2)<3.(1) 求a,b,c的值.
设函数f(x)=(ax²+1)÷(bx+c)是奇函数(a,b,c∈Z),且f(1)=2,f (2)<3.(1) 求a,b,c的值.
设函数f(x)=(ax²+1)÷(bx+c)是奇函数(a,b,c∈Z),且f(1)=2,f (2)<3.(1) 求a,b,c的值.
f(x)是奇函数,f(-x)=-f(x) (ax^2+1)/(-bx+c)=(ax^2+1)/(-bx-c) 所以c=-c c=0
f(1)=(a+1)/b=2 a+1=2b a=2b-1
f(2)=(4a+1)/2b