investigate the continuity of f ,given by f: x → { ((1−x, if x<1)),((0,if x =1)),((x^2 −3x + 2,if x >1)) :} at the point x =1


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Question Number 73565 by Rio Michael last updated on 13/Nov/19
$investigate the continuity of f ,given by f: x → { ((1−x, if x<1)),((0,if x =1)),((x^2 −3x + 2,if x >1)) :} at the point x =1$
$i n v e s t i g a t e t h e c o n t i n u i t y o f f, g i v e n b y$ $f : x \to {\begin{cases} 1 - x, i f x < 1 \\ 0, i f x = 1 \\ x^{2} - 3 x + 2, i f x > 1 \end{cases}$ $a t t h e p o i n t x = 1$
Commented byRio Michael last updated on 13/Nov/19

$t h a n k s s i r$
Commented bykaivan.ahmadi last updated on 13/Nov/19

${l i m}_{x \to 1^{-}} f (x) = {l i m}_{x \to 1^{-}} (1 - x) = 0$ ${l i m}_{x \to 1^{+}} f (x) = {l i m}_{x \to 1^{+}} (x^{2} - 3 x + 2) = 0$ $f (1) = 0$ $f i s c o n t i n u o u s a t x = 1 .$
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