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If f(x)={{:(,[x]+[-x],,,xne2 ),(," "lam...

If `f(x)={{:(,[x]+[-x],,,xne2 ),(," "lamda,,,x=2):}` then `f` is continuous at x=2, provided `lamda` is equal to -

A

1

B

0

C

-1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`becausef(x)` is continuous at x = 2
`thereforef(2)=underset(xto2)(lim)f(x)`
`rArr lamda=underset(xto2)(lim)[x]+[-x]`
`lamda`=-1
`{{:(because" we know "[x]+[-x]=0: x in1),(" "-1:x notin1):} `
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