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anonymous
 one year ago
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
anonymous
 one year ago
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

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tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1"Confirm"  This is nice. Just follow the instructions. That's what "confirm" is all about.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x) = \frac{ x7 }{ x+3 } ; g(x)=\frac{ 3x7 }{ x1 }\]

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Well? If it were f(3), what would you do?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0plug in 3 to every (x)

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Do that with g(x) and you will have f(g(x)). It's just what the notation means.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so for every (x) in f(x) i plug in 3x  7 / x  1 ?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1You have it. Let's see it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 3x  7/ x  1  7}{ 3x  7/ x  1 +3 } \]

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Horrid notation. Please use parentheses to clarify intent. f(x) = (x7)/(x+3) g(x) = (3x7)/(x1) f(g(x)) = ([(3x7)/(x1)]7)/([(3x7)/(x1)]+3) It's not pretty, but it's complete and accurate. Now, for your best algebra skills.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my apologies. can i cross out ( 3x  7 / x  1 ) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or do i multiply ( x  1 ) for numerator and denominator?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1You simplify. Let's take the numerator. \(\dfrac{3x7}{x1}  7 = \dfrac{3x7}{x1}  \dfrac{7(x1)}{x1} = \dfrac{(3x7)7(x1)}{x1}\) Keep going. We're just adding fractions.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for the numerator do i distribute?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1You do what it takes to simplify it. If the Distributive Property is appropriate, then do that. \(= \dfrac{3x  7  7x + 1}{x1}\) One step at a time.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0from that i got \[\frac{ 10x  6 }{ x  1 }\]

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Okay, now tackle the denominator.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0could you start me off so i know where to begin?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0be prepared to do a raft of algebra ready?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first we compute \[f(g(x)) = x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(g(x))=f(\frac{ 3x7 }{ x1 })\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we are going to replace all \(x\) in \(f(x)\) by \(\frac{ 3x7 }{ x1 }\) that is actually very easy for me to do here, by cutting and pasting

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1You already have the denominator. You MUST show some algebra. ([(3x7)/(x1)]+3) = \(\dfrac{3x7}{x1}+3\) Go!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x) = \frac{ x7 }{ x+3 }\]so \[f(g(x))= \frac{ \frac{ 3x7 }{ x1 }7 }{ \frac{ 3x7 }{ x1 }+3 }\]

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1THERE'S that denominator!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to get rid of that annoying compound fraction, multiply the numerator and denominator by \(x1\) (carefully using parentheses)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then multiply out, combine like terms since you know the answer will just be \(x\) you should expect an orgy of cancellation at the last couple steps

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you need the first step?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0(I would rather just find the inverse, without doing f(g(x))=x and vv, but ... \(:(\) )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0uh, i got \[\frac{ 10x  6 }{ 8 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ \frac{ \frac{ 3x7 }{ x1 }7 }{ \frac{ 3x7 }{ x1 }+3 }\] the \(x1\) will cancel top and bottom to get \[\frac{3x77(x1)}{3x7+3(x1)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now multiply out using the almighty distributive law then combine like terms

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then \[\frac{ 3x  7  7x + 1 }{ 3x  7 + 3x  1 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0forgot that distributive law already huh?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0distribute the \(7\) up top and the \(3\) below

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0starting here \[\frac{3x77(x1)}{3x7+3(x1)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(3x  7 ) ( 7x + 1) (3x  7 ) ( 3x  1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what can you get with \[7(x1)\]when you distribute?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.07x + 7 OMG . im so disappointed with myself right now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so lets back up to \[\frac{3x77(x1)}{3x7+3(x1)}\] and see what we get when we remove the parentheses by "we" i mean "you"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got, 10x /  10 which would equal to (x) so we have f(g(x)) out of the way, i started g(f(x)), coud you guide me with that to please?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok sure lets start just as before with an annoying compound fraction but try it yourself first, it is going to work almost exactly like this one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(3 (\frac{ x7 }{ x+3 })  7 (numerator) ; (\frac{ x7 }{ x+3})  1 (denominator)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me try to write it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah actually that looks good now multiply top and bottom but this time by \(x+3\) instead of \(x1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ g(x)=\frac{ 3x7 }{ x1 }\] \[ g(f(x))=\frac{ 3 \frac{ x7 }{ x+3 } 7 }{ \frac{ x7 }{ x+3 } 1 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0should have used parentheses around the first term in the top

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0multiply by \(x+3\) top and bottom what do you get before distributing etc

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this might be trickier because of the \(3\) up top so be careful with parentheses

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03(x7)  7(x+3) / (x7)  1(x+3) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now get rid of the parentheses

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you should of course just be left with some x up top and a number in the bottom that will cancel with it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.010x /  10 like before we get (x) for g(f(x)). whew! long problem lol. but thank you sooooo much for all of your time & help!! i wish i could give you more than just a medal & a fan!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0glad to help, hope you learned something (at least learned how to do these!) who studies math in late august?
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