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The domain of the function f(x)=sqrt(x^2...

The domain of the function `f(x)=sqrt(x^2-[x]^2)` , where `[x]` is the greatest integer less than or equal to `x ,` is `R` (b) `[0,+oo]` `(-oo,0)` (d) none of these

A

R

B

`[0,oo) cup Z`

C

`(-oo, 0]`

D

`R^(+)`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)= sqrt(x^(2)-[x]^(2))`, where `[*]` denotes the G.I.F
for f(x) to be real
`x^(2)-[x]^(2) ge 0`
`rArr (x+[x])" " (x [x]) ge 0`
`rArr x+[x]0, "as "x-[x] ge 0`
`rArr x in [0, oo) cup Z`
Hence domain `(f) =[0,oo) cup Z`
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