Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

Answer 1

missing something?

Answer 2

Perhaps, the functions?

Answer 3

And why is this question posted twice? You should delete one of them.

Answer 4

You should have been given f(x) and g(x)

Answer 5

I just joined yesterday i'm sorry how would i delete one? and i have a picture

Answer 6

Whoa... that's nasty.

Answer 7

For f(g(x)) you put g(x) in wherever an x is in f(x).

Answer 8

i suck at inverse problems i get confused easily, mind going step by step?

Answer 9

\[f(g(x)) = \frac{(\frac{-5x-9}{x-1})-9}{(\frac{-5x-9}{x-1})+5}\]

Answer 10

ok what's the next step

Answer 11

@satellite73
Care to assist?

Answer 12

Are you sure these are inverses? Or are you supposed to DETERMINE whether they are inverses?

Answer 13

im supposed to Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

Answer 14

Theoretically, you should be able to set
f(g(x)) = g(f(x))

Answer 15

Egads, I thought it wasn't working out when I tried it on paper, but it does.

\[f(g(x)) = \dfrac{(\dfrac{-5x-9}{x-1})-9}{(\dfrac{-5x-9}{x-1})+5}\]

\[ = \left( \dfrac{(\dfrac{-5x-9}{x-1})-9}{(\dfrac{-5x-9}{x-1})+5} \right)\frac{ x-1 }{x-1}\]

\[ = \dfrac{-5x-9-9(x-1)}{-5x-9+5(x-1)} \]

\[ = \dfrac{-14x}{-14}=x \]

Answer 16

Well, that's one direction anyway.

Answer 17

looks like you are doing fine

Answer 18

big ugly complex fraction
then an orgy of cancellation and you are done
will work the same way going the other direction

Answer 19

@satellite73 , couldn't you theoretically set them equal and then cross multiply. Then "simplify".

Answer 20

no

Answer 21

f(g(x)) = x
g(f(x)) = x
f(g(x)) = g(f(x))
That doesn't work? And if you get x = x then they are inverse?

Answer 22

ok i need to process this information, sorry i want to make sure i understand before i just runaway with the end result.this is the easiest way to do it?

Answer 23

To prove that they are inverses, you have to demonstrate that f(g(x))=x and that g(f(x))=x. That's the only way to do it. :)