The inverse notation

fSuperscript negative 1−1

used in a pure mathematics problem is not always used when finding inverses of applied problems. ​ Rather, the inverse of a function such as

Cequals=​C(q)

will be

qequals=​q(C).

The following problem illustrates this idea.

In a certain​ country, the following function represents the income tax T​ (in dollars) due for a person whose adjusted gross income is g​ dollars, where

30 comma 70030,700less than or equals≤gless than or equals≤74 comma 30074,300.

​T(g)equals=42504250plus+​0.25(gminus−30 comma 70030,700​)

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Part 1

​(a) What is the domain of the function​ T?