Question

Se considera functia bijectiva f:R->R,f(x)=1-x. Demonstrati ca functia f coincide cu inversa sa

Answer 1

$f:\mathbb_{R}\rightarrow \mathbb_{R},\quad f(x)=1-x \\ \\ 1-y = x \Rightarrow -y = x-1 \Rightarrow y = 1-x\\ \\ Se interschimba domeniul cu codomeniul \Rightarrow \\ \\ \Rightarrow f^{-1}:\mathbb_{R}\rightarrow \mathbb_{R},\quad f^{-1}(x) = 1-x$