If $f$ $(x) = \cosh x + \sinh x$ and $f$ $(x)$ $f$ $(y)$ = $f$ $(k)$ then k=

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x-y

$\frac{x}{y}$

x+y

answer is D.

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Detailed Solution

$\begin{array}{rcl} f (x) & = & \cosh x + \sinh x \\ = & \frac{e^{x} + e^{- x}}{2} + \frac{e^{x} - e^{- x}}{2} \end{array}$
$f$ $(x) = e^{x} \Rightarrow$ $f$ $(x)$ $f$ $(y) = e^{x} e^{y} = e^{x + y} =$ $f$ $(x + y)$

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