Free JEE Adv 2013 solutions
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=?
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).
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