# inverse functionWatch

#1
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
0
4 years ago
#2
To show it is invertible, could you show it is bijective?
0
4 years ago
#3
(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?
0
4 years ago
#4
(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.
0
#5
I think i probably have to use the inverse function theorem but i dont know how too
0
4 years ago
#6
(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.
0
#7
I dont know how to find the inverse of a function like that ive only ever done x= functions
0
4 years ago
#8
(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 , can you tell me what x,y,z were?
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#9
Ix=0,y=-1,z=1?
0
4 years ago
#10
(Original post by omassey)
Ix=0,y=-1,z=1?
Can you tell me, then, what are x,y,z if ?
0
4 years ago
#11
(Original post by Smaug123)
Can you tell me, then, what are x,y,z if ?
I would appreciate it.
0
4 years ago
#12
(Original post by kcorbins)
I would appreciate it.
You assume that I am any good at all at mechanics, but I'll have a look.
0
#13
X=0,y=-1,z=cube root of three
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#14
Ment c
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4 years ago
#15
(Original post by omassey)
X=0,y=-1,z=cube root of three
What are x,y,z if ?
0
#16
X=b z= cube root c so im guessing y=3b-a
0
4 years ago
#17
(Original post by omassey)
X=b z= cube root c so im guessing y=3b-a
Yes. So .
0
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