Let a function f defined by f(x)= x-xx for x≠0 and f (0) = 2. then f is

f(x)=x-|x|x⇒f(x)=1-|x|x, f(0)=2 At x=0 RHL=limx→0+1-|x|x=limx→0+1-xx=0 LHL=limx→0-1-|x|x=limx→0-1-(-x)x=2 limx→0+f(x)≠limx→0-f(x) ∴ f is discontinuous at x=0 Option (D) is correct

Let a function f defined by f(x)= x-xx for x≠0 and f (0) = 2. then f is

f(x)=x-|x|x⇒f(x)=1-|x|x, f(0)=2 At x=0 RHL=limx→0+1-|x|x=limx→0+1-xx=0 LHL=limx→0-1-|x|x=limx→0-1-(-x)x=2 limx→0+f(x)≠limx→0-f(x) ∴ f is discontinuous at x=0 Option (D) is correct

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Let a function f defined by f(x)= $\frac{x - |x|}{x}$ for x $\neq$ 0 and f (0) = 2. then f is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

continuous for all x, except at x = 0

continuous no where

continuous every where

continuous for all x, except at x = 1

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$f (x) = \frac{x - | x |}{x} \Rightarrow f (x) = 1 - \frac{| x |}{x}, f (0) = 2 At x = 0 RHL = \lim_{x \to 0^{+}} (1 - \frac{| x |}{x}) = \lim_{x \to 0^{+}} 1 - \frac{x}{x} = 0 LHL = \lim_{x \to 0^{-}} 1 - \frac{| x |}{x} = \lim_{x \to 0^{-}} 1 - \frac{(- x)}{x} = 2 \lim_{x \to 0^{+}} f (x) \neq \lim_{x \to 0^{-}} f (x) ∴ f is discontinuous at x = 0 Option (D) is correct$