Given the function $f\left(x\right)=\frac{a^x+a^{-x}}{2}\left(\mathrm{where} a>2\right).$ Then $f\left(x+y\right)+f\left(x-y\right)=$

• A

  $2f\left(x\right).f\left(y\right)$

• B

  $\begin{array}{l}f\left(x\right).f\left(y\right)\\ \end{array}$

• C

  $\frac{f\left(x\right)}{f\left(y\right)}$

• D

  none of these