A function f:R→Rf: \mathbb{R} \to \mathbb{R}f:R→R satisfies f(x)⋅f(y)=f(x+y)+f(x−y)f(x) \cdot f(y) = f(x+y) + f(x-y)f(x)⋅f(y)=f(x+y)+f(x−y) for all x,yx, yx,y. If f(0)=2f(0) = 2f(0)=2, which of the following could be f(x)f(x)f(x)?
f(x)=x2f(x) = x^2f(x)=x2
f(x)=2cos(ax)f(x) = 2\cos(ax)f(x)=2cos(ax)
f(x)=exf(x) = e^xf(x)=ex
f(x)=x+2f(x) = x+2f(x)=x+2