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The function f(x)=sin(log(x+sqrt(1+x^2))...

The function `f(x)=sin(log(x+sqrt(1+x^2)))` is (a) even function (b) odd function (c) neither even nor odd (d) periodic function

A

even function

B

odd function

C

neither even nor odd

D

periodic function

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=sin(log(x+sqrt(1+x^(2))))`
or `f(-x)=sin[log(-x+sqrt(1+x^(2)))]`
`=sin log((sqrt(1+x^(2))-x)((sqrt(1+x^(2))+x))/((sqrt(1+x^(2))+x)))`
`=sin log[(1)/((x+sqrt(1+x^(2))))]`
`=sin[-log(x+sqrt(1+x^(2)))]`
`= -sin [log(x+sqrt(1+x^(2)))]`
` :. f(-x)= -f(x)`
Therefore, `f(x)` is an odd function.
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