Pedro has created the function f (x) = the quantity of 4x-3/2 to represent the number of assignments he has completed, where x represents the number of weeks in the course. Pedro 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 equation given above can also be written as,

f (x) = (4x - 3) / 2

Then, we replace f (x) with y giving us with,

y = (4x - 3) / 2

Next, we interchange the variables such that we will be left with the equation,

x = (4y - 3) / 2

Then, we solve for the value of y using the new equation,

2x = 4y - 3

2x + 3 = 4y - 3 + 3

2x + 3 = 4y

(1/4) (2x + 3) = (4y) (1/4)

(2x + 3) / 4 = y

The inverse function is

y = (2x + 3) / 4

Substituting 30 to the value of x,

y = ((2) (30) + 3) / 4 = 30.75

Thus, the assignments that have to be finished is approximately only 30.