investigate-the-continuity-of-f-given-by-f-x-1-x-if-x-lt-1-0-if-x-1-x-2-3x-2-if-x-gt-1-at-the-point-x-1-

Question Number 73565 by Rio Michael last updated on 13/Nov/19

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 by Rio Michael last updated on 13/Nov/19

t h a n k s s i r

Commented by kaivan.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 .