Question

help me find the inverse??

Answer 1

can anybody help me with this problem. I really just need an explanation.
question is: Determine if \[f(x)= 4x+1/ x-5\] and \[g (x)= 5x-1/x+4\] are inverses of eachother. If they are not inverses explain why?

Answer 2

May I help?

Answer 3

Please do! the question is above. Im not good with math and I really just need an explanation so I can learn.

Answer 4

Thank you.
That is with my pleasure!

You will be very good at Maths In Sha' Allah!

Do you know the steps? and from where do you want to start? f(x) or g(x)?

Answer 5

I am not sure what the steps are. Could you walk me through?

Answer 6

Of course, sister!
I will not be late for any help.

Here are the steps....look at them and start to do it at one of the functions...

To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:
- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original function.

Answer 7

so to start we would make it into x=(4y+1)/(y-5)

Answer 8

or no?

Answer 9

If they are not inverses, f(g(x)) won't be equal to x.

Answer 10

And same with the contrary, g(f(x)) won't be equal to x.

Answer 11

Okay but I don't know how to start that off.

Answer 12

would you do (4(5x-1)+1)/ (x+4)-5

Answer 13

To be simple, if f(g(x)) = x = g(f(x)), they will be inverses.

Answer 14

sorry I am really not sure if I am doing this right lol

Answer 15

Do not worry, I will help.

Answer 16

"Okay but I don't know how to start that off."

Do you want to start with f(x) or g(x)?

- please proceed with one helper in order not to be confused...you choose!

Answer 17

First of all, is your original function\[\large f(x) = 4x+\frac{ 1 }{ x }-5\]

Answer 18

no, sorry I am still getting used to open study

Answer 19

4x+1 is on top, x-5 is on bottom

Answer 20

Ohh, than make sure to put parenthesis!

Answer 21

okay sorry

Answer 22

If you want to find f(g(x)), simply plug in the function g(x) into all the x in f(x)

Answer 23

so do i put the entire fraction of g(x) into where the x is in f(x)

Answer 24

Exactly :) It might be a little tricky to simplify, but if they are inverses, it would simplify to x.

Answer 25

so it would be: (4(5x-1)/(x+4)+1)/ (5x-1)/(x+4)-5)

Answer 26

let me know if i did that right

Answer 27

Yup! Looks right. Now comes the hard part. Try to simplify that as much as possible.