given-that-f-x-x-2-1-x-check-if-f-is-continuous-a-x-2-hence-write-f-x-as-a-pairwise-function-

Question Number 72838 by Rio Michael last updated on 03/Nov/19

g i v e n t h a t f (x) = \frac{∣ x - 2 ∣}{1 - ∣ x ∣}

c h e c k i f f i s c o n t i n u o u s a x = 2

h e n c e w r i t e f (x) a s a p a i r w i s e f u n c t i o n

Commented by mathmax by abdo last updated on 03/Nov/19

f (2) = 0 a n d {l i m}_{x \to 2^{+}} f (x) = {l i m}_{x \to 2^{+}} \frac{x - 2}{1 - 2} = 0

{l i m}_{x \to 2^{-}} f (x) = {l i m}_{x \to 2^{-}} \frac{- x + 2}{1 - 2} = 0

{l i m}_{x \to 2^{-}} f (x) = {l i m}_{x \to 2^{+}} f (x) = f (2) \Rightarrow f i s c o n t i n u e a t x_{0} = 2