Question

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

Answer 1

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.