Question

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.

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

Explanation:

Step1: Invert table columns

Swap "Items sold" and "Dollars" columns for the inverse table.

Step2: Rewrite equation for inverse

Start with $d = \frac{5}{2}t$, solve for $t$.
Multiply both sides by 2: $2d = 5t$
Divide by 5: $t = \frac{2}{5}d$
Rename variables for inverse function: $d^{-1}(t) = \frac{2}{5}t$ (or $f^{-1}(x) = \frac{2}{5}x$)

Answer:

a. Inverse table:

Dollars	Items sold
7.50	1
10	2
12.50	3

b. $f^{-1}(t) = \frac{2}{5}t$ (or equivalent form $t = \frac{2}{5}d$)