Answer
(a) Rate of Income Tax R(I) = $$0, if I ∈ (0, 10000]$$
$$10, if I ∈ (10000, 20000]$$
$$15, if I ∈ (20000, +\infty)$$
(b) $\$400$ Tax for $\$14000$ Income
$\$1900$ Tax for $\$26000$ Income
(c) Tax Assessed T(I) = $$0, if I ∈ (0, 10000]$$
$$10, if I ∈ (0.1I-1000, 20000]$$
$$15, if I ∈ (0.15I-2000, +\infty)$$
Work Step by Step
(a) Rate of Income Tax R(I) = $$0, if I ∈ (0, 10000]$$
$$10, if I ∈ (10000, 20000]$$
$$15, if I ∈ (20000, +\infty)$$
(b) In the case of $\$14000$ income:
the first $\$10000$ tax assessed will be (0%) $\$0$
for the next $\$4000$ tax assessed will be (10%) $\$400$
so for $\$14000$ income, total tax assessed will be $\$400$
In the case of $\$26000$ income:
the first $\$10000$ will be taxed (0%) $\$0$
the next $\$10000$ will be assessed (10%) $\$1000$ tax
and the remaining $\$6000$ will be assessed (15%) $\$900$ tax
So, for $\$26000$ income, total tax assessed will be $\$1900$
(c) Tax Assessed T(I) = $$0, if I ∈ (0, 10000]$$
$$10, if I ∈ (0.1I-1000, 20000]$$
$$15, if I ∈ (0.15I-2000, +\infty)$$
