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February 23rd, 2013, 11:24 AM  #1 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  inverse function of a multivariable function
could someone show me step by step how to find an inverse function of the following one... 
February 23rd, 2013, 06:40 PM  #2 
Member Joined: Jan 2013 Posts: 93 Thanks: 0  Re: Inverse function of a multivariable function
There is no inverse. The function is not injective, e.g. .

February 23rd, 2013, 10:57 PM  #3 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  Re: inverse function of a multivariable function
well in my notes it actually is a bijective and cont fcn (thus a homeomorphism) between , they even give that inverse but I have no clue how to find an inverse of a multivariable function 
February 24th, 2013, 09:17 AM  #4 
Member Joined: Jan 2013 Posts: 93 Thanks: 0  Re: Inverse function of a multivariable function
Then you should have stated that the domain of your function is in the first place! If you don’t state your question clearly, how are people going to understand your problem, let alone help you? So, your function is from the circle ^2+y^2=1\}" /> to the square x+y=1\}" />. Draw a straight line from the origin making an angle () anticlockwise from the positive xaxis. This line intersects and at and respectively. What does is map the first point to the second point, so the inverse maps the second point to the first point. It’s just a matter of expressing the coordinates of the first point in terms of coordinates of the second point, really. Let and . We want first to express in terms of and . Notice that . Hence Similarly 

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