Which of the following functions is an odd function?

f (x) =

constant

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f (x) = sin (log (x + \sqrt{x^{2} + 1})

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f (x) = sin x + cos x

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f (x) = 1 + x + 2 x^{3}

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Solution

The correct option is A $f (x) = sin (log (x + \sqrt{x^{2} + 1})$
For (A) $f (x) = f (- x)$ $∴ f (x)$ is an even function
For (B) $f (- x) = - f (x)$ $∴ f (x)$ is an odd function
for (C) $f (x)$ is neither odd nor even function
for (D) $f (x)$ is neither odd nor even function

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