Problem 61a

Given information

In a certain country, income tax is assessed as follows. There is no tax on income up to  . Any income over is taxed at rate of % , up to an income of % . Any income over  is taxed at % .

Step-by-step explanation

Suppose be the rate of tax and be the income, so is the function of  .

Now we have been given that, there is no tax income up to  

So  for   

If the income is in the interval  , then the tax rate is %

So  (%) for 

If the income is more than then the tax rate is %

Then    (%)   for   

Now we can write the tax rate as a function of  as follows