The function f(x)=sin(log(x+√x2+1)) is
f(x)=sin(log(x+√1+x2))
⇒f(−x)=sin[log(−x+√1+x2)]
⇒f(−x)=sinlog((√1+x2−x√1+x2+x√1+x2+x)
⇒f(−x)=sinlog[1(x+√1+x2)]
⇒f(−x)=sin[log(x+√1+x2)−1]
⇒f(−x)=sin[−log(x+√1+x2)
⇒f(−x)=−sin[log(x+√1+x2)] ⇒f(−x)=−f(x)
∴ f(x) is odd function.