Which of the functions are odd functions

f (x) = x log (\frac{1 - x^{2}}{1 + x^{2}})

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f (x) = \sqrt{1 + x + x^{4}} - \sqrt{1 - x + x^{4}}

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f (x) = \frac{x^{2} + 1}{{(x^{4} + 1)}^{2}}

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f (x) = x^{2} + cos x

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Solution

The correct options are
A $f (x) = x log (\frac{1 - x^{2}}{1 + x^{2}})$
B $f (x) = \sqrt{1 + x + x^{4}} - \sqrt{1 - x + x^{4}}$

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f (x) = {\begin{matrix} x^{4} + x^{2} - x + 2 & f o r & x \leq 1 3 x^{3} - x^{2} + x & f o r & x > 1 \end{matrix}

f (x) = \frac{1}{x^{4} + x^{2} + 1}

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(e) f(x) = log(x + $\sqrt{x^{2} + 1}$ (f) $a^{x} - a^{- x}$

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f : R \to R

f (x) = \frac{x (x^{4} + 1) (x + 1) + x^{4} + 2}{x^{2} + x + 1}

f (x)

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