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If f(x) = {((x-2)/(|x-2|)+a, ",",x lt2),...

If `f(x) = {((x-2)/(|x-2|)+a, ",",x lt2),(a+b, ",", x = 2 ),((x-2)/(|x-2|)+b, ",",x gt 2):}`
is continuous at x = 2, then a+b =

A

a=1, b=1

B

a=1, b=2

C

a=3, b=1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)={((a|x^(2)-x-2|)/(2+x-x^(2)),",",x lt 2),(b,",",x=2),((x-[x])/(x-2),",",x gt 2):}`
`f(x)={(a,",", x lt 2),(b,",", x =2),(1,",",x gt2):}`
At `=x =2`
LHL=a
RHL=1
`f(2)=b`
For continuity LHL = RHL =f(2)
a=1=b.
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