anonymous
  • anonymous
Does anyone know how to solve for the inverse of f(x) = -(1/(x-6)-4 then graph it?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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DebbieG
  • DebbieG
I'm little bit confused by your ( )'s, is the function:\[\Large f(x)=-\frac{ 1 }{x-6 }-4\]
anonymous
  • anonymous
yeah, the sheet gave us a parent functions and told us the transformations and wanted us to rewrite the equation and then graph its unverse.
anonymous
  • anonymous
inverse*

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DebbieG
  • DebbieG
You'll want to "switch and solve", meaning, write in y= form (just replace the f(x) with a y: \[\Large y=-\frac{ 1 }{x-6 }-4\] Then SWITCH the x and the y (anywhere you have a y, make it an x; anyhwere you have an x, make it a y): \[\Large x=-\frac{ 1 }{y-6 }-4\] Now, solve that^^ for y. That is your function \(\large y=f^{-1} (x)\)
anonymous
  • anonymous
I got to that stage, but i don't know what to do first. Bring the 4 over?
DebbieG
  • DebbieG
Yes, that sounds like a good start. :)
anonymous
  • anonymous
It does, but once i start breaking up the fractions it looks messy. \[x+4 = -\frac{ 1 }{ y-6 }\] then ill multiply by the denominator \[(y-6) x+4 = -1 \] and that just looks wrong to me
DebbieG
  • DebbieG
It is... :) you're missing an important set of ( )'s. :)
DebbieG
  • DebbieG
Remember, you are multiplying that WHOLE RHS by (y-6)
DebbieG
  • DebbieG
OOPS, LHS
DebbieG
  • DebbieG
(all was fine with what you did on the RHS)
anonymous
  • anonymous
\[(y-6)(x+4) = -1\] wouldnt it then look like \[yx+4y-6x-24 = -1\]
DebbieG
  • DebbieG
yes, good so far. Now remember your goal: solve for y. So keep the terms with y's on the LHS. Move anything without a y to the RHS.
DebbieG
  • DebbieG
Everything ok? (You must be typing a really long reply... lol :)
anonymous
  • anonymous
This equation makes me nervous D: \[yx+4y -6x -24 = -1\] \[yx + 4y = 6x +23\] \[\frac{ yx + 4x }{ x } = \frac{ 6x + 23 }{ x }\] \[y + \frac{ 4y }{ x } = 29 \] um i think i went wrong somewhere
anonymous
  • anonymous
lol, sorry, im getting used to this insert equation thing
DebbieG
  • DebbieG
That's ok, I was just on the edge of my seat! :) lol OK you were fine here: \(yx + 4y = 6x +23\) Perfect! Now.... you are trying to SOLVE FOR y. Dividing by x is not useful here... you have 2 terms on the LHS with a y, so you want to get y "alone", were you will only "see" ONE y. How to do that? Maybe..... factor out that y, on the LHS? \(y(x + 4) = 6x +23\) Do you see the difference, in that vs. dividing by x? Now I only have the variable y, once. I just need to finish solving for it! So what's the next step?
anonymous
  • anonymous
yes, thank you! i totally forgot about factoring :/
DebbieG
  • DebbieG
Never, ever, forget about factoring. :)
anonymous
  • anonymous
does this equation look simplified to you?\[y = \frac{ 6x + 23 }{ x + 4 }\]
DebbieG
  • DebbieG
Yes, that's fine! That's the inverse.
DebbieG
  • DebbieG
you can re-write it in the inverse notation: \(\Large f^{-1}(x) = \dfrac{ 6x + 23 }{ x + 4 }\)
DebbieG
  • DebbieG
Now, do you know how to go about graphing it? You'll want to think about: - vertical asymptotes (and behavior near them) - horizontal asymptote - x & y intercepts Those should give you a pretty good understanding of the graph. :)
anonymous
  • anonymous
I graphed it into my graphing calculate but it looks like a straight line. i think its not a function though maybe thats why it wont graph properly on my calculator
DebbieG
  • DebbieG
It is a function. It might be your viewing window.
DebbieG
  • DebbieG
Adjust your view, you may just be zoomed in too close. :)
zpupster
  • zpupster
I was following along, Debbie and you did a great job working together . this is desmos
1 Attachment
anonymous
  • anonymous
ah, i was in standard zoom
DebbieG
  • DebbieG
thanks @zupster.. and lol, I was just preparing something similar to show her.. :) see, the cool thing about a function and it's inverse is, if you look at them together, they are reflections of one another over the line y=x.
anonymous
  • anonymous
wow. im so sorry. when i wrote the equation i forgot about the horizontal compression. give me a moment to resolve it
DebbieG
  • DebbieG
http://kevinmehall.net/p/equationexplorer/#y%20=%20%286%20x+23%29/%28x+4%29|y%20=%20-1/%28x-6%29-4|y=x|[-31.622776601683793,31.622776601683793,-31.622776601683793,31.622776601683793]
DebbieG
  • DebbieG
Well, that link didn't work out too well, but you can c&p it into a new tab. :) It's cool. :)
DebbieG
  • DebbieG
I like it better with this view: http://kevinmehall.net/p/equationexplorer/#y%20=%20%286%20x+23%29/%28x+4%29|y%20=%20-1/%28x-6%29-4|y=x|[-10,15,-10,15]
anonymous
  • anonymous
i ended up with \[3y(x+4) = 6x + 23\] \[\frac{ 3y }{ 3 } = \frac{ 6x=23 }{ x+4 } \] i got stuck again
anonymous
  • anonymous
would it be multiplied by 3?
zpupster
  • zpupster
agreed, asymptotes should be shown
DebbieG
  • DebbieG
Just multiply on RHS by (1/3) :)
DebbieG
  • DebbieG
You divided by 3 on the LHS, now you need to divide by 3 on the RHS, right? But easier to "execute" that, if you think of it as multiplying by 1/3 (because, after all.... that's exactly what division by 3, IS :)
anonymous
  • anonymous
\[\frac{ 6x+23 }{ 3(x+4) }\]
anonymous
  • anonymous
does that look right?
DebbieG
  • DebbieG
From what you had above, yes. I'm not sure what your starting function was here...?
anonymous
  • anonymous
f(x) = \[-\frac{ 1 }{ 3x-6 } -4\]
anonymous
  • anonymous
sorry, i forgot about the horizontal compression applied to the parent function so i forgot to add the 3 to the original equation
DebbieG
  • DebbieG
That's OK, our first one was a good learning exercise, then. :)
anonymous
  • anonymous
yes, thank you so much!
DebbieG
  • DebbieG
Sure thing, happy to help. :)

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