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JEE MATHEMATICS MCQ: FUNCTIONS

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If f(x)=2x+2−x2,f\left( x \right) = \frac{{{2^x} + {2^{ - x}}}}{2}, then f(x+y)f(x−y)f\left( {x + y} \right)f\left( {x - y} \right) is equal to
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Correct option: A
12{f(2x)+f(2y)}\frac{1}{2}\left\{ {f\left( {2x} \right) + f\left( {2y} \right)} \right\}
Option A (12{f(2x)+f(2y)}\frac{1}{2}\left\{ {f\left( {2x} \right) + f\left( {2y} \right)} \right\}) is correct because by expanding f(x+y)f(x-y) and using the definition of f(x), we can simplify the expression to match the given option.

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