Question

f(x)=loga(x+根号x^2+1)的奇偶性

Answer 1

先求定义域.
x+√(x^2+1)≥0
x^2+1≥x^2
x可取任意实数.
f(-x)=loga(-x+√(x^2+1)
=loga[√(x^2+1)+x]^(-1)
=-loga[√(x^2+1)+x]
=-f(x)
函数f(x)为奇函数.