Chapter 1.1, Problem 59E

(a)

To determine

The piecewise-defined function T for income x where $T\left(x\right)$ is the function for tax owed on a taxable income x dollar in U.S. and the table shows the function T for single taxpayers for tax year $2015$.

If your taxable income was over …	But not over…	Your tax is…	Of the amount over …
$\$0$	$9,225$	$10\%$	$\$0$
$9,225$	$37,450$	$\$922.50+15\%$	$9,225$
$37,450$	$90,750$	$5,156.25+25\%$	$37,450$
$90,750$	$189,300$	$18,481.25+28\%$	$90,750$
$189,300$	$411,500$	$46,075.25+33\%$	$189,300$
$411,500$	$413,200$	$119,401.25+35\%$	$411,500$
$413,200$	-	$119,996.25+39.6\%$	$413,200$

(b)

To determine

To calculate: The tax owed by a single taxpayer on a taxable income of $\$45,000$ where $T\left(x\right)$ is the function for tax owed on a taxable income x dollars in U.S. and the table shows the function T for single taxpayers for tax year $2015$.

If your taxable income was over …	But not over…	Your tax is…	Of the amount over…
$\$0$	$9,225$	$10\%$	$\$0$
$9,225$	$37,450$	$\$922.50+15\%$	$9,225$
$37,450$	$90,750$	$5,156.25+25\%$	$37,450$
$90,750$	$189,300$	$18,481.25+28\%$	$90,750$
$189,300$	$411,500$	$46,075.25+33\%$	$189,300$
$411,500$	$413,200$	$119,401.25+35\%$	$411,500$
$413,200$	-	$119,996.25+39.6\%$	$413,200$