korosh23
  • korosh23
Pre-calculus 12 question!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Whats the question
korosh23
  • korosh23
One second
korosh23
  • korosh23
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korosh23
  • korosh23
It is about relation and inverse of relation
korosh23
  • korosh23
What I am wondering is how the two lines in the graph are inverses of each other?
anonymous
  • anonymous
Do u understand the inverse function?
korosh23
  • korosh23
yes
ganeshie8
  • ganeshie8
If \((a,b)\) is a point on \(f(x)\), then \((b,a)\) will be a point on its inverse.
korosh23
  • korosh23
exactly
ganeshie8
  • ganeshie8
Next, recall the transformation rule for reflection over line \(y=x\) : \[(x,y)\longrightarrow (y,x)\]
anonymous
  • anonymous
i dont understand. if you understand the inverse function, why wouldn't the graph make sense?
ganeshie8
  • ganeshie8
so, if two graphs are "symmetric" about the straight line \(y=x\), then they must be inverses of each other
korosh23
  • korosh23
I don't understand the shape of the graph, how can you tell if it is inverse?
korosh23
  • korosh23
oh I get it know @ganeshie8
ganeshie8
  • ganeshie8
lets do couple of quick examples maybe
korosh23
  • korosh23
sure
ganeshie8
  • ganeshie8
lets find inverse of below graph : |dw:1439961068302:dw|
ganeshie8
  • ganeshie8
Clearly, there is no easy way to find the inverse algebraically, you're forced to use geometry here
korosh23
  • korosh23
right
korosh23
  • korosh23
yes
ganeshie8
  • ganeshie8
can you guess how the graph of inverse should look like ?
korosh23
  • korosh23
|dw:1439954006748:dw|
ganeshie8
  • ganeshie8
That's a very good "wrong" guess, remember, we want to reflect it over line \(y=x\), not over x axis
ganeshie8
  • ganeshie8
let me just give you the answer, maybe you can try next example ok
korosh23
  • korosh23
Actually I know it, can I get one more try?
korosh23
  • korosh23
|dw:1439954141104:dw|
ganeshie8
  • ganeshie8
Excellent! |dw:1439961311805:dw|
ganeshie8
  • ganeshie8
that is a more better graph ^ observe that the line \(y=x\) passes through the origin
korosh23
  • korosh23
Ok right :)
ganeshie8
  • ganeshie8
I see that you get it, wana do one more example ?
korosh23
  • korosh23
sure :D
ganeshie8
  • ganeshie8
I'm gonna make it complicated
korosh23
  • korosh23
ok
ganeshie8
  • ganeshie8