Which of the following functions is an even function:

f (x) = sin x

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

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

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none of these

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Solution

The correct option is C $f (x) = x \frac{a^{x} - 1}{a^{x} + 1}$
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Similar questions

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

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

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) $sin x \times (e^{x} - e^{- x})$

f (x) = (1 - \frac{1}{x^{2}}) a^{x + \frac{1}{x}}, a > 0 is

\frac{a^{x + \frac{1}{x}}}{\log_{e} a}

\log_{e} a \cdot a^{x + \frac{1}{x}}

\frac{a^{x + \frac{1}{x}}}{x} \log_{e} a

x \frac{a^{x + \frac{1}{x}}}{\log_{e} a}

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