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.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose I have some function with domain R^n which maps to R^m given byf(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 definef^{-1}(x) such thatfof^{-1}(x) = I, but is I an identity matrix?. I ask this becausef(x) is a vector in R^m, I'd expect some other functiong(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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# Inverse functions in R^n

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