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. $\dfrac{f\left( x \right)}{f\left( y \right)}$