AmTran_Bus
  • AmTran_Bus
Inverse problem?
Mathematics
schrodinger
  • schrodinger
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AmTran_Bus
  • AmTran_Bus
I am willing to work it out, just need help.
AmTran_Bus
  • AmTran_Bus
The inverse is y=x^2+4, right?
geerky42
  • geerky42
What is "Theorem"?

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geerky42
  • geerky42
Correct
AmTran_Bus
  • AmTran_Bus
Hum. Well, this is online, but let me reference a book.
AmTran_Bus
  • AmTran_Bus
Maybe this?|dw:1433387173701:dw|
geerky42
  • geerky42
Looks right, but seem useless, since we can just use g(x) to derivative with.
geerky42
  • geerky42
We know \[g(x) =f^{-1}(x)= x^2+4\]
AmTran_Bus
  • AmTran_Bus
Right
geerky42
  • geerky42
well, you should be able to handle the rest.
AmTran_Bus
  • AmTran_Bus
I mean, do you just plug it in?
geerky42
  • geerky42
well, take derivative of g(x), then plug in
AmTran_Bus
  • AmTran_Bus
2x, or 8...
geerky42
  • geerky42
\(g(x) = x^2+4\) So \(g'(x) = 2x\) Now plug in \(x=4\); \[g'(4) = \boxed{8}\]
AmTran_Bus
  • AmTran_Bus
Yay!
AmTran_Bus
  • AmTran_Bus
Thank you
geerky42
  • geerky42
No problem
AmTran_Bus
  • AmTran_Bus
Hey @geerky42, would I do this the exact same way?
AmTran_Bus
  • AmTran_Bus
Its inverse is y= 2+x^2+tan(pi x/2)
geerky42
  • geerky42
That's exactly same function as original function.
geerky42
  • geerky42
its inverse should have arctan
AmTran_Bus
  • AmTran_Bus
My bad.
AmTran_Bus
  • AmTran_Bus
Can you help me continue on then? I haven't really studied that in this context.
geerky42
  • geerky42
Did you find inverse? You can swap x and y to each other, then isolate tan(...)
geerky42
  • geerky42
from there, take arctan.
AmTran_Bus
  • AmTran_Bus
Eek man, why is this one so hard?
geerky42
  • geerky42
Gee didn't realize that finding inverse would be hard lol...
geerky42
  • geerky42
@ganeshie8 Can you help?
ganeshie8
  • ganeshie8
I don't seem to remember the inverse derivative formula... deriving it is easy we knw that \[\large f(f^{-1}(x)) = x\] differentiating both sides gives \[\large f'(f^{-1}(x)){f^{-1}}'(x)=1 \] \[\large {f^{-1}}'(x) = \dfrac{1}{ f'(f^{-1}(x))}\]
ganeshie8
  • ganeshie8
plugin \(x=2\)
geerky42
  • geerky42
Hmm. What is \(f(0)\)? @AmTran_Bus
geerky42
  • geerky42
It seems that we need to use reasoning here.
AmTran_Bus
  • AmTran_Bus
I think we are maybe overthinking. Look at the choices they give as answers.
ganeshie8
  • ganeshie8
can you find f(0) ?

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