anonymous
  • anonymous
Is relation t a function? Is the inverse of relations t a function? Relation t x 0 2 4 6 y -8 -7 -4 -4
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
A. Relation t is a function. The inverse of relation t is not a functions. B. Relation t is not a function. The inverse of relation t is a function. C. Relation t is not a function. The inverse of relation t is not a function.
anonymous
  • anonymous
@UsukiDoll
UsukiDoll
  • UsukiDoll
ok so to determine a function we use the vertical line test for a graph. Similarly we use a horizontal line test for a graph to determine a one to one function. but this time we don't have a graph. Instead we have a chart. This may be a while back since I've last did charts though If I remembered correctly the function must have the x not repeating and the one to one function (inverse) must have the y not repeating

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anonymous
  • anonymous
So A?
UsukiDoll
  • UsukiDoll
yeah... I'm still trying to remember though... this was way back in 2008 when I did this.
anonymous
  • anonymous
Any help is better than no help
UsukiDoll
  • UsukiDoll
ok... now I got my memory back after I read a paragraph somewhere .. we can't have duplicates for x or y
anonymous
  • anonymous
So the answer is still A, correct?
UsukiDoll
  • UsukiDoll
there's an example in my book somewhere.. I have to find it before giving out an answer.
anonymous
  • anonymous
ok, ill wait
UsukiDoll
  • UsukiDoll
ok that was mapping and proofs. It's too strong for this problem... but I do know that we can't have anything repeating
anonymous
  • anonymous
Im gonna go with A than because the top row isn't repeating
UsukiDoll
  • UsukiDoll
the original function has a repeated value for y though..
anonymous
  • anonymous
So c?
Astrophysics
  • Astrophysics
Well for it to be a one - to - one function the x and y values are to be used only once. So if you can switch the x and y variables around to create a inverse relation, we would notice function t would not be a one - to - one function since there are two of the same y values, then we can conclude the inverse is not a function.
UsukiDoll
  • UsukiDoll
if we switch.. that would mean that there exists x values that are repeating.
anonymous
  • anonymous
So it's C @Astrophysics
UsukiDoll
  • UsukiDoll
Ok I'm seeing this horizontally .. I'm going to draw vertical |dw:1435810073365:dw|
UsukiDoll
  • UsukiDoll
alright so there are repeats.. since we can't have that.. it's not a function .
UsukiDoll
  • UsukiDoll
so switching to grab the inverse |dw:1435810139494:dw| same problem occurs
UsukiDoll
  • UsukiDoll
Since we have repetitions or duplicates of x-values with different y-values, then this relation ceases to be a function.
Astrophysics
  • Astrophysics
Well lets put it like this, |dw:1435810074921:dw| it is not a function since the x value of -4 now has two different y values, so it's not a function, I hope that makes sense
Astrophysics
  • Astrophysics
yeah exactly
anonymous
  • anonymous
So the answer is C correct?
anonymous
  • anonymous
Since if it gets reversed than there would be duplicates on x and y
anonymous
  • anonymous
@Astrophysics
UsukiDoll
  • UsukiDoll
if it's reversed we have duplicate x values if it's not reversed we have duplicate y values. either way it's not a function since each number has to be unique
Astrophysics
  • Astrophysics
Yeah, that sounds good to me, since it's not 1 - to - 1.
anonymous
  • anonymous
I have another question
Astrophysics
  • Astrophysics
Note that for a 1 - to - 1 function it has to pass both vertical and horizontal line test.
UsukiDoll
  • UsukiDoll
no... 1 to 1 is horizontal line test only
anonymous
  • anonymous
What is the inverse of the given function? y = 7x^2 - 3.
UsukiDoll
  • UsukiDoll
for graphs
UsukiDoll
  • UsukiDoll
ok first switch the x and y
UsukiDoll
  • UsukiDoll
for y=7x^2-3
Astrophysics
  • Astrophysics
I just googled it to make sure and look |dw:1435810563144:dw|
anonymous
  • anonymous
so make it x=7y^2-3
UsukiDoll
  • UsukiDoll
yes now solve for y
anonymous
  • anonymous
I wish i was as good at math as you guys are
UsukiDoll
  • UsukiDoll
If no horizontal line intersects the graph of the function more than once, then the function is one-to-one.
UsukiDoll
  • UsukiDoll
:P
UsukiDoll
  • UsukiDoll
\[x=7y^2-3\] k now solve for y
UsukiDoll
  • UsukiDoll
so we need y by itself
anonymous
  • anonymous
So how do i factor it to itself?
anonymous
  • anonymous
7*7=49 49-3=46
UsukiDoll
  • UsukiDoll
whoa.
anonymous
  • anonymous
Am i totally off
UsukiDoll
  • UsukiDoll
you want the inverse of the function. This has nothing to do with factoring
anonymous
  • anonymous
So how do i do an inverse?
Astrophysics
  • Astrophysics
Oh okkkk yes, I understand @UsukiDoll I get what you mean now haha, I kept saying it has to be 1 to 1 for it to pass both, but it just needs to pass horizontal for it to be 1 to 1 and if it passes a vertical line test it is just a function! :) Ok now I'll let you do your thing!
UsukiDoll
  • UsukiDoll
we were on the right track so our original equation y=7x^2-3 we switch the x and y x=7y^2-3 now we need to solve for y
UsukiDoll
  • UsukiDoll
to have y by itself we need to ______ 3 to both sides
anonymous
  • anonymous
add
anonymous
  • anonymous
\[y \pm \sqrt{\frac{ 3+x }{ 7}}\]
UsukiDoll
  • UsukiDoll
x+3=7y^2 \[\frac{x+3}{7}=y^2 \rightarrow \sqrt{\frac{x+3}{7}}, -\sqrt{\frac{x+3}{7}}\] my x is in a different place but it wouldn't matter since the answer is the same
anonymous
  • anonymous
yay we figured it out! *high five*
UsukiDoll
  • UsukiDoll
yay :D *high fives*
anonymous
  • anonymous
haha
anonymous
  • anonymous
It's a function if we assume \(\{0,2,4,6\}\) is the domain
Hero
  • Hero
For the original question posted, I don't agree with "C" as an answer.
anonymous
  • anonymous
How come @Hero
Astrophysics
  • Astrophysics
I don't either actually, because I kept saying 1 to 1 function, that is true it's not a 1 to 1 function, but however it is a function as the x does not repeat itself.
Hero
  • Hero
Plot each point, then perform a vertical line test: https://www.desmos.com/calculator/ogb1oqtoi2
anonymous
  • anonymous
So i was right when i said it is A?
Astrophysics
  • Astrophysics
That seems better
anonymous
  • anonymous
It's A
Hero
  • Hero
A is correct.
Astrophysics
  • Astrophysics
Sorry for the confusion @EllenJaz17 :P
anonymous
  • anonymous
Thanks guys!
anonymous
  • anonymous
No problem, at least im learning
anonymous
  • anonymous
A function is: Left total - all elements in the domain used at least once. Many to One - all elements in the domain used no more than once.
UsukiDoll
  • UsukiDoll
thanks for the memory refresher x never had repeats for the function , but switch x and y and now there are repeats
anonymous
  • anonymous
Mono, did you draw that avatar?
UsukiDoll
  • UsukiDoll
no...
Astrophysics
  • Astrophysics
Haha
UsukiDoll
  • UsukiDoll
yeah it was A for that question
UsukiDoll
  • UsukiDoll
but like I said I've done this way back . so it's not 100% until @wio showed up and I saw what he was talking about.
UsukiDoll
  • UsukiDoll
then it popped back into my mind... there's a bunch of Math topics that don't appear any more when you study further
Astrophysics
  • Astrophysics
Yeah it was a good review, I think last time I did a problem like this was in middle school
UsukiDoll
  • UsukiDoll
the graph versions.. those were the ones I knew and functions... well my book had a strong approach to it... it was about mapping... surjection/injection bijection so I highly doubt it would be used.
anonymous
  • anonymous
For the function f(x) = (8-2x)2 ,find f-1 . Determine whether f-1 is a function.
anonymous
  • anonymous
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