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If f(x)={{:(3x-4",",0lexle2),(2x+lamda",...

If `f(x)={{:(3x-4",",0lexle2),(2x+lamda",",2ltxle3):}`
is continouous at x=2, then what is the value of `lamda`?

A

1

B

-1

C

2

D

-2

Text Solution

Verified by Experts

The correct Answer is:
D
Given `f(x)={{:(3x-4",",0lexle2),(2x+lamda",",2ltxle3):}`
Also f(x) is continuous at x=2
`:.underset(xto2)limf(x)=f(2)`
Now, `f(2)=3xx2-4=6-4=2`
`impliesunderset(xto2)lim(2x+lamda)=2`
`implies4+lamda=2`
`implieslamda=-2`
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