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.

Regards,

Ashwin (IIT Madras).

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