anonymous
  • anonymous
given f(x) = (2x-2)/4 solver for f^1(3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
:/
anonymous
  • anonymous
@amistre64 @phi @jim_thompson5910 @cwrw238
amistre64
  • amistre64
when y=3, what does x have to be? or, for what value of x, does f(x) = 3

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amistre64
  • amistre64
\[f(x)=3\] \[f^{-1}(f(x))=f^{-1}(3)\] \[x=f^{-1}(3)\]
anonymous
  • anonymous
I know that.... Solving it is my issue because I can't just plug it in
amistre64
  • amistre64
sure you can, i just demonstarted that f(x) = 3
amistre64
  • amistre64
f(x) = (2x-2)/4 3 = (2x-2)/4
amistre64
  • amistre64
the value of x is equal to f^-1(3)
amistre64
  • amistre64
even if we dont go that route, but replace x by f^-1(3) \[f(x)=\frac{2x-2}{4}\] \[f(f^{-1}(3))=\frac{2(f^{-1}(3))-2}{4}\] \[3=\frac{2(f^{-1}(3))-2}{4}\] solve for f^(-1)(3)
anonymous
  • anonymous
If I plug it in, I get 1. i don't know what the ^-1 means
amistre64
  • amistre64
^-1 is inverse notation ....
anonymous
  • anonymous
I know that
amistre64
  • amistre64
youre giving me mixed results here ... you either know or you dont; it cant be both :/
anonymous
  • anonymous
Let me rephrase. I KNOW what the ^-1 IS but I don't know what to do with it
amistre64
  • amistre64
hmm, you recall that y = f(x) right?
anonymous
  • anonymous
yep, sorry for the miscommunication
amistre64
  • amistre64
to undo the f, we apply its inverse; so f^-1 each side \[y=f(x)\] \[f^{-1}(y)=f^{-1}(f(x))\] \[f^{-1}(y)=x\] letting y = 3 \[f^{-1}(3)=x\] and since y = f(x), let f(x) = 3 and solve for x
amistre64
  • amistre64
hmm, you recall that y = f(x) right?
anonymous
  • anonymous
so the Y actually equals 3? Although I don't have a Y? Seems weird that they'd give me that
amistre64
  • amistre64
f(x) is a curve in the xy plane; for some value of x, we can measure the value of the curve, and relate it to the y axis.
phi
  • phi
you could think like this f(x) is a rule that changes x into y the inverse goes the other way, given y, you find x
amistre64
  • amistre64
|dw:1378406020372:dw|
anonymous
  • anonymous
Why is this question so complex? s: I have at least three others like this
amistre64
  • amistre64
its trying to get you to understand some basic concepts which havent really been addressed that clearly to you
amistre64
  • amistre64
a function has a specific value attrbuted to a given value of x, we can measure that value f(a), using the y axis such that y = f(a), for some x=a
anonymous
  • anonymous
Exactly. And to anyone's surprise, this actually isn't in my lesson. It explains functions and inverse but it doesn't give examples. Math is my worst subject so I don't understand any of it.
amistre64
  • amistre64
lets define a function as the path to get from the couch to the refridderator ... the inverse function is how you get back to the couch again
amistre64
  • amistre64
|dw:1378406257168:dw|
amistre64
  • amistre64
thats all in inverse does is get you back to where you started
amistre64
  • amistre64
so if we made it to y=f(x)=3. then the inverse process f^-1(3) will get us back to the value of x that got us there to start with
anonymous
  • anonymous
i know. It's the reverse basically
amistre64
  • amistre64
soo, \[3 = \frac{2x-2}{4}\] what value of x got us to f(x) = 3?
anonymous
  • anonymous
the inverse?
anonymous
  • anonymous
what you're asking is unclear
amistre64
  • amistre64
solve for x ...
anonymous
  • anonymous
I don't know how e_e I've never had to solve for x with a fraction
amistre64
  • amistre64
i would suggest getting rid of the /4 by multiplying each side by 4 ... this is just your algebra rules in practice is all; the name of the variable is rather inconsequential
anonymous
  • anonymous
but the X is on the right side of the equal sign, rather than the left. What other "side" and I supposed to multiply besides 3? 3*4 is 12, okay... What about that remaining? I'm sure there's a better way to explain this..
amistre64
  • amistre64
do you agree that a=b is the same as b=a ? does it matter what side of the equal side anything is really on? It matter when programing a computer program, but only because the computer is very precise in how it reads the program
amistre64
  • amistre64
\[3 = \frac{2x-2}{4}\] \[3*4 = \frac{2x-2}{4}*4\] \[12 = \frac{2x-2}{1}*1\] \[12 = 2x-2\]etc...
amistre64
  • amistre64
what would you suggest we do next?
anonymous
  • anonymous
No, the side doesn't matter but my question still remains the same as to what else is there to multiply besides 3. From there, my only guess is to add 12 to both sides the divide by 2(x)
anonymous
  • anonymous
edit: why is 4*4 = 1? S: you only took care of the denominator and not the numerator equation
amistre64
  • amistre64
4/4 = 1 this is pretty basic stuff that i am assuming you already know \[\frac{2x-2}{4}*4\] \[(2x-2)*\frac{1}{4}*4\] \[(2x-2)*\frac{4}{4}\] \[(2x-2)*\frac{1}{1}\] \[(2x-2)*{1}\] \[2x-2\]
anonymous
  • anonymous
What the hell....... You JUST said "i would suggest getting rid of the /4 by multiplying each side by 4" NOW you're saying DIVIDE? Could you /please/ make up your mind? Division and multiplication are two different things!
amistre64
  • amistre64
i just multiplied the right side by 4, and drew out all the little intermediary processes that show how the right side gets worked out ....
anonymous
  • anonymous
I'd like to get help from someone else if you don't mind.
amistre64
  • amistre64
i dont mind
phi
  • phi
when you have time, watch Khan's videos start with http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same--thing-to-both-sides--simple-equations they are all short
anonymous
  • anonymous
Halfway into the video, I look at the title. I know things should be done to both sides. @phi I'm not really sure why you sent that to me. Amistre is making the question more confusing and it's clear. First he says multiplication, then he tells me division. I know it's against the site, but I'm really only looking for an answer. I have a lot more questions to go and I can't continue to be stuck on this one.
anonymous
  • anonymous
and being unclear* I just want an answer x.x
phi
  • phi
The "answer" is knowing how to do the problem if you don't know how, you should try to learn how.
anonymous
  • anonymous
._________________________. Really. Really? Nobody is getting anywhere with this so I'm closing it.
phi
  • phi
if you know what's in that video, move on to more complicated ones http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/v/two-step-equations at some point you will find where the videos are teaching you what you don't yet know.
amistre64
  • amistre64
the problem already had a division by 4 on the right side; to get rid of it you need to multiply both sides by 4. These are basic and fundamental algebra skills.

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