query: Function with the property $f\circ f=-id$
positive_passages.docid: 11453
positive_passages.text: Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
negative_passages.docid: 143610
negative_passages.text: If $f^3=\rm id$ then it is identity function
negative_passages.docid: 22758
negative_passages.text: If $\operatorname{ran} F \subseteq \operatorname{dom} G$, then $\operatorname{dom}(G \circ F) = \operatorname{dom} F$.
negative_passages.docid: 98559
negative_passages.text: subtlety of self-defined function and its evaluation
negative_passages.docid: 110704
negative_passages.text: Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 39090
negative_passages.text: Finding functions such that $f(g(x)) = f(x)g(x)$
negative_passages.docid: 139436
negative_passages.text: Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 97184
negative_passages.text: Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
negative_passages.docid: 154001
negative_passages.text: $(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
negative_passages.docid: 26687
negative_passages.text: Show that $f$ maps the unit circle to itself
negative_passages.docid: 40070
negative_passages.text: Is there a real-valued function $f$ such that $f(f(x)) = -x$?
negative_passages.docid: 24306
negative_passages.text: Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
negative_passages.docid: 17343
negative_passages.text: Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
negative_passages.docid: 27251
negative_passages.text: Holomorphic function with $f\circ f=f$
negative_passages.docid: 28286
negative_passages.text: About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$