Which of the following function(s) is/are odd function(s) ?

f (x) = \frac{x^{3}}{2^{| x |} + sec x}

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

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

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None of these

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Solution

The correct options are
A $f (x) = \frac{x^{3}}{2^{| x |} + sec x}$
C $f (x) = \frac{(e^{x} - 1)}{(e^{x} + 1)}$

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Similar questions

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = $x^{2} | x |$ (b) f(x) = $e^{x} + e^{- x}$

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

(g) f(x) = $sin x + cos x$ (h) $sin x \times (e^{x} - e^{- x})$

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = $x^{2} | x |$ (b) f(x) = $e^{x} + e^{- x}$

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

(g) f(x) = $sin x + cos x$ (h) $sin x \times (e^{x} - e^{- x})$

1. f (x) = x^{3}, x ϵ R

2. f (x) = sin x, - π / 2 < x < π / 2

3. f (x) = e^{x}, x ϵ R

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

Prove that the following functions do not have maxima or minima:

(i) f(x) = e^x (ii) g(x) = logx

(iii) h(x) = x³ + x² + x + 1

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