Answer
a. $f(x)=\begin{cases}
0.1x \text{ for } x\leq 20000\\
2000+0.2(x-20000) \text{ for }x \gt 20000
\end{cases}$
b. for $x\leq 2000$, $ y=10x$.
for $y\gt 2000$, $y=5x+10000$.
c. $y=60000$.
Work Step by Step
a.
$f(x)=$$\begin{cases}
0.1x \text{ for } x\leq 20000\\
2000+0.2(x-20000) \text{ for }x \gt 20000
\end{cases}$
b.
$f^{-1}$,
$x=$$\begin{cases}
0.1y \text{ for } y\leq 20000\\
2000+0.2(y-20000) \text{ for }y \gt 20000
\end{cases}$,
for $y\leq 20000$,
$x=0.1y, y=10x, 0\leq x\leq 2000$.
for $y\gt 20000$,
$x=2000+0.2(y-20000)$,
$x=2000+0.2y-4000$,
$x=0.2y-2000$,
$y=\frac{x+2000}{0.2}$, $y=5x+10000,x>2000$.
c.
$x=10000$, $y=5(10000)+10000=60000$.
thus, It would require an Income of $60000$ to pay $10000$ in tax.
