Question

The inverse notation f^-1 used in a pure mathematics problem is not always used when finding inverses of applied problems. Rather, the universe of a function such as C =C (q) will be q=q(C). The following problem illustrates this idea.
In a certain country the following function represents the income tax T (in dollars) do for a person who is adjusted gross income is G dollars where 30,500 ? g ? 74,100.
T(g)=4250+0.25(g-30,500)
A.) what is the domain of the function T?
B.). Given that the income tax do T is an increase in linear function of adjusted gross income G find the range of the function T
C.) find adjusted gross income G as a function of income tax T . what are the domain and the range of this function?

Answer 1

9514 1404 393

Answer:

  A)  30,500 < G ≤ 74,100

  B)  4,250 < T ≤ 15,150

  C) G = 4(T -4,250) +30,500; domain: 4,250 < T ≤ 15,150; range: 30,500 < G ≤ 74,100

Step-by-step explanation:

A) The domain of T is given in the problem statement:

  30,500 < G ≤ 74,100

__

B) The range of T is the set of values of T that correspond to the domain values. The minimum will be T(30,500) = 4,250. The maximum will be T(74,100) = 4,250 +0.25(74,100 -30,500) = 15,150.

  4,250 < T ≤ 15,150

__

C) The inverse function can be found by solving the given equation for G.

  T = 4250 +0.25(G -30500)

  T -4250 = 0.25(G -30500)

  4(T -4250) = G -30500

  G = 30,500 +4(T -4,250)

The domain and range of this function are the range and domain of the function T(g), respectively.

Answer 2

Answer:

[ 2, $\infty$ )

Explanation:

In photo below