The technician at a North American retail franchise tells me that, "Firefox is on it's way out", is this true?

Sorry, what do you mean by this:

Last Friday I sought advice on an alternative to the new Firefox format. ... The Yahoo takeover of its 47.099 format seems to verify this.

Is there a problem with unwanted Yahoo pages appearing in your Firefox?

Or with the radically changed Yahoo! toolbar??

What did you want to fix???

Regarding Firefox being "on its way out," Google has been tremendously successful with Chrome. I think all other browsers are being used less now. But Mozilla isn't giving up on Firefox yet.

Tasiturn said

Last Friday I sought advice on an alternative to the new Firefox format. The store's Technician told me that, "Firefox was on its way out". The Yahoo takeover of its 47.099 format seems to verify this. Is it it true? - Why?

Firefox format ? and The Yahoo takeover of its 47.099 format ?

Firefox is the name of this web browser as it is not a search engine or website as some people for various reasons thought Firefox was.

It is still strong and is Mozilla.org 's main product as they have no plans to discontinue the desktop Firefox web browser anytime soon or in future.

As for Yahoo in Firefox, the en-US locale of Firefox browser has Yahoo as the default search engine since Firefox 34.0 Released back on December 1, 2014 and other locales have different search engines as default also now. Google is no longer the global default search engine in Firefox but is still one of the search engines that Firefox come with you can use. https://blog.mozilla.org/blog/2014/11/19/promoting-choice-and-innovation-on-the-web/

You can change the search engine if you like https://support.mozilla.org/en-US/kb/use-search-bar-firefox if this is the case.

Yahoo did change their toolbar extension for Firefox to a more simpler version shortly before Firefox 48.0 however neither Mozilla nor the Firefox web browser had anything to do with this Yahoo toolbar change.