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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

`(0, oo)`

B

`(-oo, 0)`

C

`(-oo, oo)`

D

None of these

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • The domain of the function f(x)=sqrt(x^(2)-[x]^(2)) , where [*] greatest integer function less than or equal to x:

    A
    R
    B
    `[0,oo) cup Z`
    C
    `(-oo, 0]`
    D
    `R^(+)`

  • The domain of the function f(x) = sqrt((4-x^(2))/([x]+2)) where [x] denotes the greatest integer less than or equal to x,is

    A
    `[-1, 2]`
    B
    `(-oo, -2 )`
    C
    `(-oo, -2) uu [-1,2]`
    D
    none of these

  • The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

    A
    `{x:x=(2n+1) pi, n in Z} cup { x : 2 m pi le x lt 2m pi+(pi)/(3), m in Z}`
    B
    `{x:x=2n pi , n in Z} cup { x: 2 m pi lt(x =2n pi) , n in Z} cup { x : 2 m pi lt x lt 2m pi +(pi)/(3), m in Z }`
    C
    `{x:(2n+1) pi, n in Z} cup { x : 2m pi lt x lt 2 m pi +(pi)/(3), m in Z}`
    D
    none of these

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