选C
f(x)定义域为R
f(-x)+f(x)
=ln[-x+√(x²+1)]+ln[x+√(x²+1)]
=ln[(x²+1)-1]
=ln1
=0
f(-x)=-f(x)
D中函数定义域为x≠1不关于原点对称,非奇偶函数.