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1) alex's house 2) alex' house when the noun ends with the letter 's' or 'x', do i need to put 's' after an apostrophe or not

I remember i read some rules related to this in my school gram. There are two correct ways to form this phrase On my behalf on behalf of me on behalf of someone is a phrase The of someone part can be put between on and behalf using a determiner instead of a pronoun. If yes, what is the substitution idiom for expressing heavy rain?