已知函數(shù)f(x)=x+1/x (1)求證函數(shù)f(x)為奇函數(shù) (2)用定義證明:函數(shù)f(x)在(1,+∞)上是增函數(shù).
已知函數(shù)f(x)=x+1/x (1)求證函數(shù)f(x)為奇函數(shù) (2)用定義證明:函數(shù)f(x)在(1,+∞)上是增函數(shù).
(1)f(-x) = (-x) + 1/(-x) = -(x+ 1/x) = -f(x)
(2)這是對勾函數(shù)
設(shè)1
f(x1)-f(x2)=(x1-x2)+1/x1-1/x2=(x1-x2)-(x1-x2)/(x1x2)=(x1-x2)[1-1/(x1x2)]
因?yàn)?
所以得證