Question

Can somebody please help me with these last 4! Im stuck, I've tried over and over :(

Given the function f(x) = The quantity of 3x minus 4, divided by 5, which of the below expressions is correct?

f−1(x) = The quantity of 5x plus 4, divided by 3.
f−1(x) = The quantity of 5x minus 4, divided by 3.
f−1(x) = The quantity of negative 3x minus 4, divided by 5.
f−1(x) = The quantity of 4 minus 3x, divided by 5.

Answer 1

kinda too many questions per thread. I will help you with the first one here, if you do not mind.

Answer 2

Thats fine, I can post in a seperate thread if needed :) thank you so much

Answer 3

\(\large\color{black}{ \displaystyle f(x) = \frac{ 3x - 4}{5} }\)

Answer 4

first, replace f(x) with "y" (for convenience)

then change x and y with each other (put x instead of y, and vice versa)

Answer 5

and then solve for y in your new equation.
(after you find the y, denote this y as \(f^{-1}(x)\) )

Answer 6

can you do the first step
1) replace \(f(x)\) with y

Answer 7

So now it is
x= 3y-4 / 5

Answer 8

yes x=(3y-4)/5

Answer 9

then you need to isolate the y

Answer 10

How do I do that?

Answer 11

Do i multiply by 5?

Answer 12

yes, that is good!

Answer 13

multiply times 5 on both sides

Answer 14

So it would look like
(5) x = 3y-4 / 5 (5)

Answer 15

yes,

\(\large\color{black}{ \displaystyle x=\frac{ 3y-4 }{5} }\)

\(\large\color{black}{ \displaystyle x\color{blue}{\times 5}=\frac{ 3y-4 }{5} \color{blue}{\times 5} }\)

Answer 16

continue please:)

Answer 17

Now im stuck at this part :(

Answer 18

the 5's on the right cancel, and the left side is just 5x

\(\large\color{black}{ \displaystyle x \color{blue}{\times 5}=\frac{ 3y-4 }{\cancel{5}}\color{blue}{\times \cancel{5}} }\)

\(\large\color{black}{ \displaystyle 5x = 3y-4 }\)

Answer 19

making sense?

Answer 20

Yes, now that makes sense

Answer 21

ok, now isolate the y

Answer 22

(or, "solve for y" -- same thing)

Answer 23

Would I start by adding the 4 to 5x?

Answer 24

yes, good!

Answer 25

what is your equation now?

Answer 26

9x = 3y?

Answer 27

oh, 5x and 4 aren't like terms

Answer 28

I mean 9 = 3y :)

Answer 29

\(\large\color{black}{ \displaystyle 5x = 3y-4 }\)

you are adding 4 to both sides.

\(\large\color{black}{ \displaystyle 5x\color{red}{+4} = 3y-4 \color{red}{+4} }\)

what happens to the right side?
the left side side remains the way it is right now, because \(5x\) and \(4\) can't be added together.

Answer 30

the right side cancels out so we're left with 5 x +4 /3 would be the final asnwer?

Answer 31

that would be the final answer.

Answer 32

nicely done

Answer 33

Thank you so much! :) I think I understand this mess a little better now lol

Answer 34

\(\normalsize\color{ slate }{\Huge\displaystyle {\bbox[5pt, lightcyan ,border:2px solid black ]{ {\rm f}^{-1}(x)=\frac{5x+4}{3} }}}\)

Answer 35

basically, all you need to do in general is:

1) replace f(x) with y.
2) change x and y (replace them with each other- x for y, and y for x)
3) {solve for/ isolate the} y (this is the difficult part)
4) after you found y, denote this y as an inverse function, because this y is indeed the inverse function. So instead of y, write \({\rm f}^{-1}(x)\).

Answer 36

glad that it helped. I have to depart for some time.... see you.

Answer 37

I think I got it, thank you again :)