Question

Please help!
Sam has created the function f(x) = the quantity of 4x minus 3, divided by 2 to represent the number of assignments he has completed, where x represents the number of weeks in the course. Sam discovers that, using the inverse function to solve for x = 32, he can predict when he will have 32 assignments completed. Explain to Sam how to accomplish this, using complete sentences.

Answer 1

f(x) = $\frac{4x-3}{2}$

f⁻¹(x) ⇒ $x = \frac{4y-3}{2}$

           2x = 4y - 3

     2x + 3 = 4y

    $\frac{2x+3}{4} = y$

f⁻¹(32) ⇒  $\frac{2(32)+3}{4} = y$

              $\frac{64)+3}{4} = y$

              $\frac{67}{4} = y$  

              16.75 = y

Answer: Sam will be able to complete 32 assignments in 16.75 weeks