In all cities in this state which now have or may hereafter have more than one hundred thousand inhabitants and less than five hundred thousand inhabitants, it shall be the duty of the county assessor, collector of the revenue, and the officer charged with the duty of auditor of such county or any of them to perform the services for such city pertaining to like offices when required by such city so to do, and such city or cities are authorized and empowered to require such officers of the county or any of them to perform the duties for the city pertaining to such offices at such times, under such terms, in such manner and for such compensation as such city may provide.