Final answer:
The LH stimulates the formation of the corpus luteum during the luteal phase of the menstrual cycle. It is not linked directly with the liver, development of the hypothalamus, or water balance in the kidney.
Step-by-step explanation:
Luteinizing hormone (LH) has multiple roles in the human reproductive system, but when it comes to the options provided, the correct answer is: (d) formation of the corpus luteum. LH stimulates the formation of the corpus luteum from the follicular tissue that is left behind after ovulation.
During the luteal phase of the menstrual cycle, after the follicle releases the egg, the remaining tissue transforms into the corpus luteum under the influence of LH. This structure then secretes progesterone to prepare the uterus for possible pregnancy. While it is true that LH (together with Follicle Stimulating Hormone or FSH) stimulates the growth of ovarian follicles during the follicular phase, the direct function of LH as mentioned in the question is the formation of the corpus luteum.