Question

Pedro has created the function f(x) = (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

y=(4x-3)/2
y is number of assignments where x represents number of weeks in the course
you want to find the number of weeks when the number of assignments is 30 (that is when y is 30)
But it tells us to find the inverse function
where the y and x are vise verse in meaning
so you start by solving the following for y: x=(4y-3)/2
where y represents the number of weeks when x represents the number of assignments

Answer 2

So when you solve that for y.
Plug in 30 for x to find y

Answer 3

okay so correct me if I'm wrong because I'm pretty sure I am

Answer 4

30 = (4y - 3)/2 and divide both sides by 2
15 = 4y - 3, then you add 3 from each side
18 = 4y, and divide by 4
y = 9/2

Answer 5

well that is right
except I think they said they wanted you to find the inverse function

Answer 6

almost right *

Answer 7

2*30 is actually 60 not 15

Answer 8

so you would have 60=4y-3

Answer 9

but anyways i still think you are suppose to find the inverse function

Answer 10

30 = (4y - 3)/2 and *MULTIPLY* both sides by 2

but you want to solve x=(4y-3)/2 this first for y.

Answer 11

wait so you multiply both sides by 2 and get 60 = 8y - 6/4? and then what?

Answer 12

?

Answer 13

no

Answer 14

I multiplied both sides by 2
60=4y-3

Answer 15

\[x=\frac{4y-3}{2} \\ 2 \cdot x =2 \cdot \frac{4y-3}{2} \\ \text{ you know that } \frac{2}{2}=1 \\ 2 \cdot x =\frac{2}{2} (4y-3) \\ 2x=1(4y-3) \\ 2x=4y-3\]

Answer 16

and that's the inverse function?

Answer 17

no you have to solve for y

Answer 18

I did one step for you

Answer 19

I multiplied 2 on both sides

Answer 20

you did the other steps above
the adding 3 on both sides
then the dividing 4 on both sides
do that here

Answer 21

x = (4y - 3)/2 then you multiply both sides by 2
2x = 2/2(4y - 3) and since 2/2 = 1 we are left with
2x = 4y - 3 now all you have to do is plug 30 in for x to find y
2(30) = 4y - 3
60 = 4y - 3 add 3 to both sides
63 = 4y divide by 4
y = 15.75

Answer 22

???

Answer 23

why don't you want to solve 2x=4y-3 for y?

Answer 24

2x=4y-3 add 3 to both sides
2x+3=4y then you divide 4 on both sides
(2x+3)/4=y
g(x)=(2x+3)/4 is the inverse function
replace the number of assignments x with 30 to find the number of weeks y

Answer 25

so (2(30)+3)/4?

Answer 26

yes you evaluate that
which you already did without finding the inverse function
--

Answer 27

so the answer is y = 15.75?

Answer 28

well that is part of your solution

Answer 29

your problem asked to find the inverse function which I did for you above

and then use your inverse function to find the number of weeks when the number of assignments is 30

and then part of your solution is also using complete sentences to describe how you found the inverse function

Answer 30

okay, thank you