Question

Find the inverse of the function.

f(x) = 4x - 6

Not a one-to-one function
f-1(x) = quantity x plus six divided by four
f-1(x) = x divided by four plus six
f-1(x) = quantity x minus six divided by four

Answer 1

@Hero

Answer 2

@Vocaloid

Answer 3

@Isry

Answer 4

@Hero

Answer 5

First change f(x) to y, then swap the x and y. Solve for y. Finally change to f^(-1)(x)

Answer 6

So would this be D?

Answer 7

Have you solved it yet or are you just guessing?

Answer 8

well im doing this in my head so mainly guess...but i also suck terribly at this so i dont really know how to solve for y here

Answer 9

If you change f(x) to y what will you have afterwards? Can you type it here please?

Answer 10

Yea then we would have y = 4x - 6 right?

Answer 11

Great, now swap the positions of x and y. Post the result here.

Answer 12

ok so now its x = 4y - 6

Answer 13

Excellent. Now add 6 to both sides. Post the result here.

Answer 14

x = 4y?

Answer 15

Did you add 6 to BOTH sides?

Answer 16

yes according to what i was taught...im guessing what i was taught was wrong

Answer 17

Okay, if you start with x = 4y - 6 then add 6 to both sides, what would that look like? Can you show me your process?

Answer 18

so 6 + x = 4y - 6 + 6

Answer 19

Great. Now simplify that. Post it here.

Answer 20

x6 = 4y?

Answer 21

sorry man math is not my best subject

Answer 22

Explain why you remove the PLUS on the left side.

Answer 23

im not sure thats just how all the examples in my lessons show it so i thought it was right...would it be 6 + x = 4y then?

Answer 24

Yes, correct. It is proper to write the variable first. In that case, you would have
x + 6 = 4y. Now the last step is to do what? Any idea what the last step might be?

Answer 25

no...

Answer 26

wait do we subtract x from each side?

Answer 27

Divide both sides by 4. Remember, the goal was to isolate y because once you did that you would have found the inverse of that. Go ahead and divide both sides by 4. Let me know what you get.

Answer 28

i dont know...but i think i know the answer to the question...as i think i just have to find the equation

Answer 29

can you help me with one more question maybe...

Answer 30

Are you telling me that with one step remaining, you are unable to figure out how to express the correct answer? Can you at least make the attempt please. I'd prefer if you used the drawing tool for this. Thanks.

Answer 31

well the end i came up with is

Answer 32

sorry on a laptop

Answer 33

so the right side i got y as the 4 kinda cancels out and the left side i cant solve

Answer 34

Yes, that is correct. So using \(\LaTeX\) to express the correct result we get \(y = \dfrac{x + 6}{4}\) but remember we replace \(y\) with \(f^{-1}(x)\) to get \(f^{-1}(x) = \dfrac{x + 6}{4}\)

Answer 35

awesome thank you so much

Answer 36

as i said i kinda have on more if you can help me with that one

Answer 37

one*

Answer 38

Are you sure you're not able to finish it up on your own?. Go ahead, post it, then post all your steps. Make sure to tag me AFTER you have finished with your attempt. Deal?

Answer 39

no like i dont even know where to start im supposed to explain how two things are inverses f(x)= 4 over x and g(x) = 4 over x and i dont know where i am supposed to start with that like at all

Answer 40

Post it as a separate post my friend.