Recall from the video above that if $f$:$R^{d}R$ and $K(x,x^{\text{'}})$ is a kernel, so is

widetilde$(K)(x,x^{\text{'}})=f(x)K(x,x^{\text{'}})f(x^{\text{'}}).$

If there exists $(x)$ such that

$K(x,x^{\text{'}})=(x)*(x^{\text{'}}),$

then which of the following $$ gives

widetilde$(K)(x,x^{\text{'}})=(x)*(x^{\text{'}})?$

$(x)=f(x)K(x,x)$

$(x)=f(x)K(x,x^{\text{'}})$

$(x)=f(x)$

$(x)=f(x)(x)$