Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x: f(x) =x-7/x+3 and g(x) = -3x-7/x-1

Answer 1

f(g(x)) = x let's do this one first. since g(x) took the place of x in f(x) you have to put in g(x) in place of x in equation f(x).
What I mean here is...
f(g(x))=g(x)-7/g(x)+3=(-3x+7/x+1)-7/(-3x+7/x+1)+3 simplify that equation and you should get f(g(x))=x
for the second part g(f(x))=x, do the same thing but now put in f(x) in g(x).

Answer 2

you have it wrong it is g(x)=-3x-7/x+1 not -3x+7/x+1

Answer 3

also i had it wrong suppose to be x-1 under the -3x-7

Answer 4

\[f(x)= \cfrac{x-7}{x+3}\]\[g(x)=\cfrac{-3x-7}{x+1}\]\[f(g(x)) = \cfrac{\cfrac{-3x-7}{x+1} -7}{\cfrac{-3x-7}{x+1} +1}\]\[ f(g(x)) =\cfrac{\cfrac{-3x-7-7x-7}{x+1}}{\cfrac{-3x-7+x+1}{x+1}}\]\[f(g(x)) = \cfrac{\cfrac{-10x-14}{x+1}}{\cfrac{-2x-6}{x+1}} \]\[f(g(x)) = \cfrac{-10x-14}{-2x-6}\]\[ f(g(x)) = \cfrac{-2(5x+7)}{-2(x+3)}\]\[f(g(x)) = \cfrac{5x+7}{x+3}\]

Answer 5

omg i messed up....

Answer 6

try it again?

Answer 7

made a typo there but I used the same idea as Jhannybean

Answer 8

\[f(g(x)) = \cfrac{\cfrac{-3x-7}{x+1} -7}{\cfrac{-3x-7}{x+1} +3}\]\[f(g(x)) =\cfrac{\cfrac{-3x-7-7x-7}{x+1}}{\cfrac{-3x-7+3x+3}{x+1}}\]\[f(g(x))= \cfrac{-10x-14}{-4}\]\[f(g(x))= \cfrac{5x-7}{2}\] and you will get the same result solving \(g(f(x))\)

Answer 9

I also have a problem with that one because it is as shown

\[g(f(x))=\frac{ -3(\frac{ x-7 }{ x+3 })-7 }{ \frac{ x-7 }{ x+3 }-1 }\]

Answer 10

And i got no idea how to reduce that

Answer 11

keep spirit :)
@Jhannybean

Answer 12

Maybe theyre not inverses of each other.... hmm... lets see!

Answer 13

\[g(f(x)) = \cfrac{-3\left(\cfrac{x-7}{x+3}\right)-7}{\cfrac{x-7}{x+3}+1}\]\[g(f(x)) = \cfrac{\cfrac{-3x+21-7x-21}{x+3}}{\cfrac{x-7+x+3}{x+3}}\]\[g(f(x)) = \cfrac{-3x-7x}{2x-4}\]\[g(f(x)) = \cfrac{-10x}{2x-4}\]\[g(f(x)) = \cfrac{-10x}{2(x-2)}\]\[g(f(x))= \cfrac{-5x}{x-2}\]

Answer 14

so are they inverses?

Answer 15

I don't think they are.....

Answer 16

hmm unusual. Most the questions i was askedi n the past involving this they were

Answer 17

I am kind of unsure atm xD

Answer 18

Eh if all else fails i can submit my assignment and just get a 34/35 asuming i got rest all ok

Answer 19

ok well i put this down and see wht i get

Answer 20

thanks!

Answer 21

One minute...

Answer 22

ok I will wait

Answer 23

http://fooplot.com/plot/fwj9gaersw they don't look like inverses of eachother, perhaps @RadEn can help clarify this?

Answer 24

no they dont...this is quite odd to be honest xD

Answer 25

yes, f and g are inverses. maybe just wrong in simplication :)

Answer 26

well when simplified doing f(g(x)) and g(f(x)) they should both equal x

Answer 27

yes, i got that

Answer 28

but it looks too complicated to even think that they do xD that is the problem and jhannybean's work looks all ok

Answer 29

Can you point out where i went wrong? xD

Answer 30

g(f(x)) = ...../(x-7)/(x+3) + 1

the last should -1 not + 1

Answer 31

ahh yes

Answer 32

hopefully i will see xD

Answer 33

Ok got first one to equal x now all i got is the g(f(x))