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If f:R rarrR is defined by f(x)=[x-3]+|x...

If `f:R rarrR` is defined by `f(x)=[x-3]+|x-4|` for `x in R`, then `lim_(xrarr3^(-)) f(x)` is equal to (where `[.]` represents the greatest integer function)

A

`-2`

B

`-1`

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Given that,
`f(x)=[x-3]+[x-4]`
`therefore" "underset(xrarr3^(+))limf(x)=underset(xrarr3^(-))lim([x-3]+[x-4])`
`=underset(hrarr0)lim([3-h-3]+|3-h-4|)`
`=underset(hrarr0)lim([-h]+1h)`
`=-1+1+0=0`
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Knowledge Check

  • If f: R rarr R is defined by f(x) = [ x -3] + | x-4| for x in R then lim_(x rarr 3^(-)) f(x) is equal to

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    B
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