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

f⁻¹(x) ⇒
`x = (4y-3)/(2)`

2x = 4y - 3

2x + 3 = 4y

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

f⁻¹(32) ⇒
`(2(32)+3)/(4) = y`

`(64)+3)/(4) = y`

`(67)/(4) = y`

16.75 = y

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