Question

question
question 1b

1. find the inverse of each function. when the function is given as a table, find the inverse as a table. when the function is an equation, find the equation of the inverse.¹

a.

items sold	0	1	2	3

b. $d = \frac{5}{2}t$

Explanation:

Part a:

Step1: Identify original function pairs

Original pairs: $(0,5), (1,7.50), (2,10), (3,12.50)$

Step2: Swap variables for inverse

Inverse pairs: $(5,0), (7.50,1), (10,2), (12.50,3)$

Step3: Format inverse as table

Dollars	Items sold
7.50	1
10	2
12.50	3

Part b:

Step1: Swap variables $d$ and $t$

$t = \frac{5}{2}d$

Step2: Solve for $d$

Multiply both sides by $\frac{2}{5}$:
$d = \frac{2}{5}t$

Step3: Rename for inverse function

Let inverse be $t(d)$, so $t = \frac{2}{5}d$

Answer:

a.

Dollars	Items sold
7.50	1
10	2
12.50	3

b. $t = \frac{2}{5}d$