Relative pronoun "in which" vs. relative adverb "where" II

I am confused by why the following sentence is connected with "in which".

The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.

Why this sentence can be connected by using "in which"?

Also I learned that "[preposition] + [which]" can be substituted by relative adverbs. For example, "This is a house in which I live" is equal to "This is a house where I live". The sentence can be divided into "This is a house" & "I live in the house.", and it is easy to concatenate with relative clauses.

So adding to the question, can in which be replaced with "where"?

If you are familiar with mathematics, I also ask that if "We define the function f by f(x)=ax+b, where a and b are constants." can be substituted by in which?