Question

已知f（x+

1

x

）=x³+

1

x3

，則f（x）=

x³-3x

．

Answer 1

分析：由f（x+

1

x

）=x³+

1

x3

=(x+

1

x

)(x2 -1+

1

x2

)=(x+

1

x

)[(x+

1

x

)2- 3]，能求出f（x）．

解答：解：∵f（x+

1

x

）=x³+

1

x3

=(x+

1

x

)(x2 -1+

1

x2

)
=(x+

1

x

)[(x+

1

x

)2- 3]
=(x+

1

x

)3-3(x+

1

x

)，
∴f（x）=x³-3x．
故答案為：x³-3x．

點評：本題考查函數解析式的求解及常用方法，是基礎題．解題時要認真審題，仔細解答．