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Addition of two real functions
If the function $f(x)=\dfrac{{{a}^{x}}+{{a}^{-x}}}{2},\left( a>2 \right),$ then \[f\left( x+y \right)+f\left( x-y \right)\] is equal to
A.\[2f\left( x \right)f\left( y \right)\]
B. \[f\left( x \right)f\left( y \right)\]
C. $\dfrac{f\left( x \right)}{f\left( y \right)}$
D. None of these

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