Confused on this function question...

Question

For income x (in dollars), a particular state's income tax T (in dollars) is given by

T(x) =

0.028 x if 0≤ x≤ 4,000

112+0.035(x−4,000) if 4,000< x≤ 24,000

812+0.050 (x−24,000) if x>24,000

What is the tax on an income of $42,000?

I figured the bottom function would be used as x = income and x > 24,000. My answer was 0.04076 or 4.08%. I was told this was incorrect and that the middle function in the given T(x) should be used. Am I missing something?

Answer 1

Your answer looks correct to me, except that I would have expressed the result as $1712 rather than 4.08%.

Is it possible you were supposed to solve the problem for x=24,000 instead of x=42,000? Then the middle equation would apply.