Solve the problem.The following piecewise function gives the tax owed, T(x), by a single taxpayer on a taxable income of x dollars.T(x) = (i) Determine whether T is continuous at 7593.(ii) Determine whether T is continuous at 31,687.(iii) If T had discontinuities, use one of these discontinuities to describe a situation where it might be advantageous to earn less money in taxable income.

What will be an ideal response?


(i) continuous
(ii) continuous
(iii) Answers may vary. For instance if T(x) were partly defined as follows: 
T(x) = 
then there would be a discontinuity at 7593 and a large jump in tax owed for an amount just slightly larger than $7593 in taxable income.

Mathematics

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