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Question: Answered & Verified by Expert
If function fx=x-xx,x<0 =x+xx,x>0 =1,x=0, then
MathematicsContinuity and DifferentiabilityMHT CETMHT CET 2019 (Shift 2)
Options:
  • A limx→0-fx does not exist
  • B limx→0+fx does not exist
  • C fx is continuous at x = 0
  • D limx→0-fx≠limx→0+fx
Solution:
1673 Upvotes Verified Answer
The correct answer is: fx is continuous at x = 0
Given function,
fx=x-xx,x<0
=x+xx,x>0,x=0
Now, at x = 0
LHL=limx→0fx=limx→0x-xx
limx→0x--xx=limx→0x+1=1
RHL=limx→0+fx=limx→0+x+xx
=limx→0x+1=1f0=1
∴limx→0-fx=limx→0fx=f0=1
⇒fx is continuous at x = 0

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