inverse function Watch

omassey
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I have no idea for this can someone help.
consider the functionf:R^3 to R^3 defined by f (x,y,z)=(3x-y,x,z^3) a) prove it is invertable and find its inverse fiunction g
b) what are the points in R^3 where the inverse function g is differentiable
thankyou
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rayquaza17
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To show it is invertible, could you show it is bijective?
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tombayes
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(Original post by omassey)
I have no idea for this can someone help.
consider the functionf:R^3 to R^3 defined by f (x,y,z)=(3x-y,x,z^3) a) prove it is invertable and find its inverse fiunction g
b) what are the points in R^3 where the inverse function g is differentiable
thankyou
do you know the inverse function theorem?
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Smaug123
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(Original post by tombayes)
do you know the inverse function theorem?
Does that help here? The IFT is a property of *local* inverses, not global ones.

OP, I think the way to go is just to construct the inverse function directly.
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omassey
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I think i probably have to use the inverse function theorem but i dont know how too
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Smaug123
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(Original post by omassey)
I think i probably have to use the inverse function theorem but i dont know how too
Unless I'm being really silly, you don't need the IFT. You just need to write down the inverse and try differentiating it.
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omassey
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I dont know how to find the inverse of a function like that ive only ever done x= functions
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Smaug123
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(Original post by omassey)
I dont know how to find the inverse of a function like that ive only ever done x= functions
Given that f(x,y,z) = (1,0,1), can you tell me what x,y,z were?
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omassey
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Ix=0,y=-1,z=1?
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Smaug123
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(Original post by omassey)
Ix=0,y=-1,z=1?
Can you tell me, then, what are x,y,z if f(x,y,z) = (1,0,c)?
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1374786
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(Original post by Smaug123)
Can you tell me, then, what are x,y,z if f(x,y,z) = (1,0,c)?
Please help me with my mechanics question: http://www.thestudentroom.co.uk/show....php?t=3005989
I would appreciate it.
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Smaug123
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(Original post by kcorbins)
Please help me with my mechanics question: http://www.thestudentroom.co.uk/show....php?t=3005989
I would appreciate it.
You assume that I am any good at all at mechanics, but I'll have a look.
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omassey
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X=0,y=-1,z=cube root of three
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omassey
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Ment c
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Smaug123
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(Original post by omassey)
X=0,y=-1,z=cube root of three
What are x,y,z if f(x,y,z) = (1, b, c)?
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omassey
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X=b z= cube root c so im guessing y=3b-a
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Smaug123
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(Original post by omassey)
X=b z= cube root c so im guessing y=3b-a
Yes. So f^{-1}(a,b,c) = (b, 3b-a, c^{\frac{1}{3}}).
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