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Find the domain of f(x)=sqrt(([x]-1))+sq...

Find the domain of `f(x)=sqrt(([x]-1))+sqrt((4-[x]))` (where [ ] represents the greatest integer function).

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We have `f(x)=sqrt([x]-1)+sqrt(4-[x])`
Clearly f(x) is defined if `[x] -1 ge 0 " and " 4-[x] ge0`
` :. 1 le [x] le 4`
`implies 1 le x lt5`
Hence domain of f(x) is `[1,5)`.
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