veja se ajuda:
//desktop
document.querySelector("#cabecalho .conteiner").style.cssText = "background-image: url('https://suaimagem.jpg'); background-repeat: no-repeat; background-position: center center; background-size: cover;";
//mobile
document.querySelector("#cabecalho > div.conteiner > div").style.cssText = "background-image: url('https://suaiamgem.jpg'); background-repeat: no-repeat; background-position: center center; background-size: cover;";
Obs: Use imagens diferentes, pois são tamanhos totalmente diferentes.