f-R-R-is-defined-by-f-x-1-1-if-x-Z-if-x-Z-Is-f-continuous-at-x-1-and-x-3-2-

Question Number 25825 by rita1608 last updated on 15/Dec/17

f : R \to R i s d e f i n e d b y

f (x) = {\underset{- 1 i f x \notin Z}{1} if x \in Z

I s f c o n t i n u o u s a t x = 1 a n d x = - \frac{3}{2} \int ?

Answered by prakash jain last updated on 15/Dec/17

\lim_{x \to 1^{+}} f (x) = \lim_{h \to 0^{+}} f (1 + h) = - 1

∵ (1 + h) \notin Z as h \to 0

similary

\lim_{x \to 1^{-}} f (x) = - 1

f (1) = 1

LHL = RHL \neq f (1) function

is not continuius at 1 .

for 3 / 2

LHL = RHL = - 1

f (3 / 2) = - 1

f (x) is continous at 3 / 2