"let g be the function from F(R) to RxR defined by g(f)=( f(0), f(1) ). Prove that g is a homomorphism from F(R) onto RxR, and describe its kernel"

I'm trying to find the kernel. so the kernel is kerf={x in F(R); g(x)= e_RxR} ? Wouldn't it just be (0,0) ? If this is right how do i prove this? If this is wrong then how do i find the kernel?