inverse function

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?

I think i probably have to use the inverse function theorem but i dont know how too

I dont know how to find the inverse of a function like that ive only ever done x= functions

Ix=0,y=-1,z=1?

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/showthread.php?t=3005989
I would appreciate it.

X=0,y=-1,z=cube root of three

X=b z= cube root c so im guessing y=3b-a