Question

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

Answer 1

\[f(x)=(x-7)/(x+3) and g(x)=(-3x-7)/(x-1)\]

Answer 2

the first step i know is to write.... im working on it...

Answer 3

yeah its ugly

Answer 4

\[((-3x-7)/(x-1)-7)/ ((-3-7)/(x-1)+3)\]

Answer 5

i get that...but i dont know hw to simplify it all

Answer 6

is that f(g(x)) or g(f(x))?

Answer 7

thats f(g(x))

Answer 8

\[f(x)=\frac{x-7}{x+3}\\g(x) = \frac{-3x-7}{x-1}\\
f(g(x)) =\frac{g(x)-7}{g(x)+3}=\frac{\frac{-3x-7}{x-1}-7}{\frac{-3x-7}{x-1}+3} \]
is this what you did?

Answer 9

Yep

Answer 10

ok
\[\frac{\frac{-3x-7}{x-1}-7}{\frac{-3x-7}{x-1}+3}\]
multiply everything by (x-1)
\[\frac{(x-1)\frac{-3x-7}{x-1}-7(x-1)}{(x-1)\frac{-3x-7}{x-1}+(x-1)3}=\\\frac{-3x-7-7x+7}{-3x-7+3x-3}=\frac{-10x}{-10}=x\]

Answer 11

oh boy...tiny writing

Answer 12

mac or pc?

Answer 13

pc XD but i got it

Answer 14

do the steps make sense?

Answer 15

completely :D now can you help me with g(f(x))?

Answer 16

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

Answer 17

multiply every term by (x+3) and tell me what you have

Answer 18

ok :) let me try :)

Answer 19

not the right thing.. thats for sure....

Answer 20

\[\frac{-3(x-7)-7x-21}{x-7-x-3}=\frac{-10x}{-10}=x\]

Answer 21

this is after you multiply everything by (x+3)

Answer 22

I hope you understand this, because they were exactly alike, and you should be able to do it now. Unless you don't understand something in which case tell me

Answer 23

how did you get the numerator to that...becuse it cancels out its denominator but where did the -7x and 21 come from

Answer 24

NEVERMIND

Answer 25

\[\frac{-3\frac{x-7}{x+3}(x+3)-7(x+3)}{\frac{x-7}{x+3}(x+3)-1(x+3)}=\frac{-3(x-7)-7x-21}{x-7-x-3}=\frac{-3x+21-7x-21}{x-7-x-3}\]

Answer 26

ok:)

Answer 27

Thank you!

Answer 28

np