Income Taxes The U.S. federal income tax is a function of taxable income. Write $T(x)$ for the tax owed on a taxable income of $x$ dollars. For tax year 2015 the function $T$ for a single taxpayer was specified as follows:
$$\begin{array}{|c|c|c|c|}\hline \begin{array}{c}\text { If your tax- } \\\text { able income } \\\text { was over ...}\end{array} & \begin{array}{c}\text { But not } \\\text { over ... }
\end{array} & \text { Your tax is ... } & \begin{array}{c}\text { Of the } \\\text { amount } \\
\text { over ... }\end{array} \\
\hline \$ 0 & 9,225 & 10 \% & \$ 0 \\\hline 9,225 & 37,450 & \$ 922.50+15 \% & \$ 9,225 \\\hline 37,450 & 90,750 & 5,156.25+25 \% & \$ 37,450 \\\hline 90,750 & 189,300 & 18,481.25+28 \% & \$ 90,750 \\
\hline 189,300 & 411,500 & 46,075.25+33 \% & \$ 189,300 \\\hline 411,500 & 413,200 & 119,401.25+35 \% & \$411,500 \\\hline 413,200 & - & 119,996.25+39.6 \% & \$ 413,200 \\\hline\end{array}$$
a. Represent $T$ as a piecewise-defined function of income $x$.
b. Use your function to compute the tax owed by a single taxpayer on a taxable income of $\$ 45,000 .$