f(x)=[x]+[-x] when xis not equal to 2 and A ,when X =2 if fx is continuous at x=2 thwn the value of A=?

2 years ago


Answers : (2)


Hi Koushik,


Ih you note

f(x) as x tends to 2 from the right ie 2+

f(2+) = 2-3 = -1

And f(x) as x tends to 2 from the left ie 2-

f(2-) = 1-2 = -1.


So f(2) = A = -1 for f(x) to be continuous at 2.


Hope it helps.

Wish you all the best.



Ashwin (IIT Madras).

2 years ago

For continuity lim x->2+ f(x) = f(2) = lim x-> 2-

Evalutaing left hand limit: 

When x->2-: [x]+[-x] = [2-h]+[-(2-h)] =1+[-2+h]=1-2=-1

Evaluating right hand limit

When x->2+ : [2+h]+[-2-h]= 2+(-3)= -1 

therefore f(2) = -1 to mk the function continuous

2 years ago

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