x +√(x^2+1)＞x +√x^2=x+|x|≥0,
所以函数定义域是R.
f(x)=ln(x +√(x^2+1))
f(-x)=ln(-x +√(x^2+1))
注意到(x +√(x^2+1)) •(-x +√(x^2+1))
=(x^2+1)- x^2=1
所以f(-x)=ln(-x +√(x^2+1))=ln1/(x +√(x^2+1))
= -ln(x +√(x^2+1))=- f(x)
∴函数是奇函数.