A simplified income tax considered in the U.S. Senate in 1986 had two tax brackets. Married couples

Question:

A simplified income tax considered in the U.S. Senate in 1986 had two tax brackets. Married couples earning $29,300 or less would pay 15% of their income in taxes. Those earning more than $29,300 would pay $4350 plus 27% of the income over $29,300 in taxes. Let T(x) be the amount of taxes paid by someone earning x dollars in a year.

(a) Find

(b) Find

(d) Sketch a graph of T(x).
(e) Identify any x-values where T is discontinuous.
(f) Let A(x) = T(x)/x be the average tax rate, that is, the amount paid in taxes divided by the income. Find a formula for A(x).

(g) Find