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Given the function f(x)=(a^x+a^(-x))/2(w...

Given the function `f(x)=(a^x+a^(-x))/2(w h e r ea >2)dotT h e nf(x+y)+f(x-y)=` `2f(x)dotf(y)` (b) `f(x)dotf(y)` `(f(x))/(f(y))` (d) none of these

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The correct Answer is:
A
We have
`f(x+y)=f(x-y)=(1)/(2)[a^(x+y)+a^(-x-y)+a^(x-y)+a^(-x+y)]`
`=(1)/(2)[a^(x)(a^(y)+a^(-y))+a^(-x)(a^(y)+a^(-y))]`
`=(1)/(2)(a^(x)+a^(-x))(a^(y)+a^(-y))=2f(x)f(y)`
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