Multiclass Feats Question

When you take a new class do you get a new feat for being 1st level of that new class.
From the example in PFRPG Core p. 30:
"For example, let’s say a 5th-level fighter decides to
dabble in the arcane arts, and adds one level of wizard
when he advances to 6th level. Such a character would
have the powers and abilities of both a 5th-level fighter
and a 1st-level wizard, but would still be considered a 6thlevel
character. (His class levels would be 5th and 1st, but
his total character level is 6th.) He keeps all of his bonus
feats gained from 5 levels of fighter, but can now also cast
1st-level spells and picks an arcane school. He adds all
of the hit points, base attack bonuses, and saving throw
bonuses from a 1st-level wizard on top of those gained
from being a 5th-level fighter."

The fighter get 3 bonus feats for being fighter 5, 3 feats for being 5th level, and we'll make the fighter human so +1 for a total of 7 feats.
When this character takes the wizard class, 1st level classes get 1 feat. Does this character get 1 more feat, for a total of 8, just for multiclassing?

Thanks

A character doesn't get a feat for becoming 1st level in a class. He gets one for being 1st level as a character. The exceptions to this are classes that specifically list a bonus feat at 1st level, such as the fighter and the wizard (who gets Scribe Scroll, specifically). Were this fighter taking a level in bard, not wizard, he'd be getting no feats as bards get no feat at 1st level. You're confusing 1st level character with 1st level in a given class. Your example would have 8 feats, but only because 1st level wizards get a bonus feat.

No. Feats are gained based on Character level, not class level (unless they're class features like a Fighter's bonus feat)

No, the feat is for 1st character level, not first level of every class; if he takes two levels in wizard to get to 7th level (fighter 5/wizard 2) then he gets the feat for 7th level.

Your multi-class character is is a 6th level character, with five levels in fighter and one in wizard, he is only ever a first level character once.

Your multi-class character is is a 6th level character, with five levels in fighter and one in wizard, he is only ever a first level character once.

I get it, total class levels...