How to prove that if the function y = f (x) is odd in R and there is an inverse function, then the inverse function is also odd

Y = f (x) is an odd function. If f (x) = y = - f (- x) f (- x) = - y, let its inverse function be f '(x) y = f' (x), that is, f (y) = x, then f (- y) = - f (y) = - x, f '(- x) = - y, so f' (x) = - f '(- x) is proved

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