Question

Please help? :C
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

Answer 1

\[\frac{ \frac{ -3x -7 }{ x-1 } -7}{x+3 }\]

Answer 2

Sorry i do not know give it some goodies so that people want it like if you answer it i will fan you and give you a medal

Answer 3

That's poopy. :p

Answer 4

@whpalmer4

Answer 5

@jdoe0001 Please?

Answer 6

It might help if I put the question correctly...
\[f(x)=\frac{ x-7 }{ x+3 } g(x)=\frac{ -3x-7 }{ x-1 }\]

Answer 7

@sourwing

Answer 8

lemme do the first one, that is f( g(x) ) = x

Answer 9

well just plug g in for x of f, then simply and do the other way around

Answer 10

Thank you. :) I can't seem to figure out how to get past (-10x)/(x-1)/(x+3).

Answer 11

I did, but I can't get it to the point where it equals x...

Answer 12

one sec

Answer 13

\(\bf f(x)=\cfrac{ x-7 }{ x+3 } \qquad {\color{red}{ g(x)}}=\cfrac{ -3x-7 }{ x-1 }

\\ \quad \\ \quad \\
f(\quad g(x)\quad )=\cfrac{ ({\color{red}{ \frac{ -3x-7 }{ x-1 }}})-7 }{ ({\color{red}{ \frac{ -3x-7 }{ x-1 }}})+3 }\implies
\cfrac{ \frac{ -3x-7 }{ x-1 }-7 }{ \frac{ -3x-7 }{ x-1 }+3 }
\\ \quad \\
f(\quad g(x)\quad )=\cfrac{\frac{-3x-7-7(x-1)}{x-1}}{\frac{-3x-7+3(x-1)}{x-1}}\implies \cfrac{\frac{-3x-7-7x+7}{x-1}}{\frac{-3x-7+3x-3}{x-1}}
\\ \quad \\
f(\quad g(x)\quad )=\cfrac{-3x\cancel{-7}-7x\cancel{+7}}{\cancel{x-1}}\cdot \cfrac{\cancel{x-1}}{\cancel{-3x}-7\cancel{+3x}-3}\)

see what that gives you

Answer 14

Oh.. You put it where both x's are. Hang on.

Answer 15

yes

Answer 16

Okay, so you wind up with -10x/-10, which simplifies down to just x. Right?

Answer 17

yes, \[\frac{-10x}{-10} = x\]

Answer 18

yeap

Answer 19

so \(\bf {\color{red}{ f(x)}}=\cfrac{ x-7 }{ x+3 } \qquad g(x)=\cfrac{ -3x-7 }{ x-1 }
\\ \quad \\ \quad \\

g(\quad f(x)\quad )=\cfrac{ -3({\color{red}{ \frac{ x-7 }{ x+3 }}})-7 }{ ({\color{red}{ \frac{ x-7 }{ x+3 }}})-1 }\implies

\cfrac{ \frac{ -3x+21 }{ x+3 }-7 }{ \frac{ x-7 }{ x+3 }-1 }\)

Answer 20

the previous compound function, that is f( g(x) ) gave us "x"
thus that means that they're indeed inverse of each other
thus this one should too

Answer 21

Oh, gawsh. Thank you so much! God bless you!

Answer 22

yw