Question

函数y=log以a为底（x+根号下x²+1）的奇偶性为?

Answer 1

首先判断定义域

定义域 x∈R 满足关于原点对称.

f(x)

= log(a ,x + √(x² + 1) ) (逗号前面的表示底数,后面的表示真数)

= log(a ,√(x² + 1) + x )

f(-x)

= log(a ,√(x² + 1) - x )

f(x) + f(-x)

= log(a ,√(x² + 1) + x ) + log(a ,√(x² + 1) - x )

= log(a , 1)

= 0

所以 f(-x) = -f(x)

所以原函数为奇函数.