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Let f(x)={(x-4)/(|x-4|)+a ,x<4a+b ,(x-4)...

Let `f(x)={(x-4)/(|x-4|)+a ,x<4a+b ,(x-4)/(|x-4|)+b ,x >4` Then `f(x)` is continous at `x=4` when `a=0,b=0` b. `a=1,b=1` c. `a=-1,b=1` d. `a=-1,b=-1`

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Verified by Experts

The given function can be written
`f(x)={(x-4)/(|x-4|)+a ,x<4a+b ,(x-4)/(|x-4|)+b ,x >4`
LHL at `x=4`,
`lim​_(x→4−)f(x)`
`=lim_(h→0)​f(4−h)`
...
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