Question

已知函数f(x)=ln(x+根号下x^2+1) (1)证明f(x)为奇函数。（2）若f(x)=ln(2+根号5,求x的值

求详细过程，谢啦

Answer 1

x+根号下x^2+1>0恒成立，定义域为R，关于原点对称
f(-x)=ln(-x+根号下x^2+1)
=ln[(-x+根号下x^2+1)*(x+根号下x^2+1)/(x+根号下x^2+1)]
=ln[1/(x+根号下x^2+1)]
=ln[(x+根号下x^2+1)^(-1)]
=-ln(x+根号下x^2+1)
=-f(x) f(x)为奇函数

f(x)=ln(2+根号5),
x+根号下x^2+1=2+根号5
x=2