determine-wether-or-not-the-function-f-where-f-x-2x-1-0-x-lt-2-7-x-2-x-lt-4-3x-4-4-x-lt-6-is-continuous-in-the-interval-0-6-

Question Number 73572 by Rio Michael last updated on 13/Nov/19

d e t e r m i n e w e t h e r o r n o t t h e f u n c t i o n f, w h e r e

f (x) = {\begin{cases} 2 x + 1, 0 ⩽ x < 2 \\ 7 - x, 2 ⩽ x < 4 \\ \frac{3 x}{4}, 4 ⩽ x < 6 \end{cases}

i s c o n t i n u o u s i n t h e i n t e r v a l [0, 6 [

Commented by kaivan.ahmadi last updated on 13/Nov/19

{l i m}_{x \to 2^{-}} f (x) = {l i m}_{x \to 2^{+}} f (x) = 5

{l i m}_{x \to 4^{-}} f (x) = {l i m}_{x \to 4^{+}} f (x) = 3

\Rightarrow f i s c o n t i n u o u s .