In a certain country, the tax on incomes less than or equal to €20,000 is 10%. F

label Algebra
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(a) Find a function f that gives the income tax on an income x in €. Express f as a piecewise defined function. 

f(x) = 
     if 0 ≤ x ≤ 20,000
     if x > 20,000
 

(b) Find 
f −1.
 
f −1(x) = 
     if 0 ≤ x ≤ 2000
     if x > 2000
Mar 1st, 2015

f(x) = 0.1 * x                                 if  0<  x <= 20,000

f(x) = 2000+ 0.5 *(x-20000)                       if x > 20,000

x= y*10                                                   if  0< y <=2000

x= (y-2000)/0.5+20000                          if y >2000

f-1 (x) = 10x                                          if  0< x < =2000

f-1 (x) = 20000+(x-2000)* 2                    if x > 2000


Mar 1st, 2015

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Mar 1st, 2015
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Mar 1st, 2015
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