If you have more than one question, you need to make separate posts.

To answer your first question, T(x) is the amount of tax liability based on an individual's income. This income tax liability is based on the income of the individual. The specific type of system described here is called a **progressive tax**, and is used in many of the countries in the world, where an individual pays more tax when more money is earned.

If the income `x` is less than 90,000, then the liability (amount owed to the government) is 5% of the income. That is, the amount owed is

`T(x)=0.05x`

If the income is more than 90000 but less than 140000, then the individual owes 5% of the income from the first 90000, then an additional 15% of the income from over 90000. That is, the first 90000 owes 4500, and the additional amount is 0.15(x-90000). This gives:

`T(x)=0.15(x-90000)+4500`

If the income is more than 140000 but less than 220000, then the tax owed is 25% of the amount earned over 140000, plus an additional 12000, which is 4500 from the first 90000 and 15% from the next 50000. This gives

`T(x)=0.25(x-140000)+12000`

Finally, if the individual makes more than 220000, then the remaining income over 220000 is taxed at 35%, with an additional 32000, which consists of 4500 from the first 90000, 7500 from the next 50000 and 20000 from the next 80000. This gives

`T(x)=0.35(x-220000)+32000`

**This is a progressive tax system and requires more tax owed if an individual earns more income.**