query: Some examples of functions that are their own inverse?
positive_passages.docid: 44148
positive_passages.text: Functions that are their own inverse.
negative_passages.docid: 88559
negative_passages.text: Which function (s) is(are) the k-th derivative of itself?
negative_passages.docid: 107400
negative_passages.text: Can there be an injective function whose derivative is equivalent to its inverse function?
negative_passages.docid: 7036
negative_passages.text: Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
negative_passages.docid: 56805
negative_passages.text: Why isn't the inverse of the function $x\mapsto x+\sin(x)$ expressible in terms of "the functions one finds on a calculator"?
negative_passages.docid: 132907
negative_passages.text: The inverse of a bijective holomorphic function is also holomorphic
negative_passages.docid: 3801
negative_passages.text: Functions that take rationals to rationals
negative_passages.docid: 103568
negative_passages.text: Possibility of finding a such function?
negative_passages.docid: 86919
negative_passages.text: When (and more importantly, why) does $AA^T$ have an inverse?
negative_passages.docid: 53376
negative_passages.text: A continuous, nowhere differentiable but invertible function?
negative_passages.docid: 13193
negative_passages.text: Does a inverse function need to be either surjective or injective?
negative_passages.docid: 141286
negative_passages.text: When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
negative_passages.docid: 58561
negative_passages.text: Right and left inverse
negative_passages.docid: 10850
negative_passages.text: Are all functions that have an inverse bijective functions?
negative_passages.docid: 41043
negative_passages.text: example of discontinuous function having direction derivative
negative_passages.docid: 47166
negative_passages.text: Is there a function whose inverse is exactly the reciprocal of the function, that is $f^{-1} = \frac{1}{f}$?
negative_passages.docid: 45280
negative_passages.text: Is there an Inverse Gamma $\Gamma^{-1} (z) $ function?