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Let f(x) = log ({x}) [x] g (x) =log (...

Let ` f(x) = log _({x}) [x]`
` g (x) =log _({x})-{x}`
`h (x) log _({x}) {x}`
where `[], {}` denotes the greatest integer function and fractional part function respectively.
If `A = {x:x in ` domine of `f (x))) and B {x:x` domine of `g (x)}` then `AA x in (1,5), A -B` will be :

A

`(2,3)`

B

`(1,3)`

C

`(1,2)`

D

None of these

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Let f(x) = log _({x}) [x] g (x) =log _({x})-{x} h (x) log _({x}) {x} where [], {} denotes the greatest integer function and fractional part function respectively. Domine of h (x) is :

    A
    `[2,oo)`
    B
    `[1,oo)`
    C
    `[2,oo)-{I}`
    D
    `R ^(+) -{I}`

  • Let f(x) = log _({x}) [x] g (x) =log _({x})-{x} h (x) log _({x}) {x} where [], {} denotes the greatest integer function and fractional part function respectively. For x in (1,5)the f (x) is not defined at how many points :

    A
    5
    B
    4
    C
    3
    D
    2

  • f(x)=[x^(2)]-{x}^(2), where [.] and {.} denote the greatest integer function and the fractional part function , respectively , is

    A
    continuous at x=1,-1
    B
    continuous at x=-1 but not at x=1
    C
    continuous at x=1 but not at x=1
    D
    discontinuous at x=1 and x=-1

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