Pedro has created the function f (x) = 4x-3/2 to represent the number of assingments he has completed where x represents the number of weeks in the course Person discovers that using the inverse function to solve for x=30, he can predict when he will have 30 assignments completed explain to Pedro how to accomplish this using complete sentences

The given function is

f (x) = 4x - 3/2

where

f (x) = number of assignments completed

x = number of weeks required to complete the assignments

We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.

The procedure is as follows:

1. Set y = f (x)

y = 4x - 3/2

2. Exchange x and y

x = 4y - 3/2

3. Solve for y

4y = x + 3/2

y = (x + 3/2) / 4

4. Set y equal to f⁻¹ (x)

f⁻¹ (x) = (x + 3/2) / 4

5. Find f⁻¹ (30)

f⁻¹ (30) = (30 + 3/2) / 4 = 63/8 = 8 (approxmately)

Answer:

Pedro needs about 8 weeks to complete 30 assignments.