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## Main Question or Discussion Point

Sorry if this is the wrong place for my question, I'm having difficulty on a conceptual level getting my head round inverse functions and compositions of functions in R^n. I'm failing to understand my lecture notes as a result.

Suppose I have some function with domain R^n which maps to R^m given by

I'm clearly missing something. Can anyone throw me any hints or direct me to some online material that would help me (I have a book on the way in the post)

Suppose I have some function with domain R^n which maps to R^m given by

**f**(__x__) =**f**[x^{1},x^{2},...,x^{n}]^{T}=[f^{1}(__x__),f^{2}(__x__),...,f^{m}(__x__)]^{T}it seems reasonable that you'd want to define**f**^{-1}(__x__) such that**f**o**f**^{-1}(__x__) = I, but is I an identity matrix?. I ask this because**f**(__x__) is a vector in R^m, I'd expect some other function**g**(**f**(__x__)) would also be a vector (as opposed to a matrix).I'm clearly missing something. Can anyone throw me any hints or direct me to some online material that would help me (I have a book on the way in the post)

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