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Let S denotes the set consisting of four...

Let S denotes the set consisting of four functions and `S = { [x], sin^(-1) x, |x|,{x}}` where , `{x}` denotes fractional part and [x] denotes greatest integer function , Let A, B , C are subsets of S.
Suppose
A : consists of odd functions (s)
B : consists of discontinuous function (s)
and C: consists of non-decreasing function(s) or increasing function (s).
If `f(x) in A nn C, g(x) in B nnC, h (x) in B" but not C and " l(x) in ` neither A nor B nor C .
Then, answer the following.
The function l (x) is

A

periodic

B

even

C

odd

D

neither odd nor even

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let S denotes the set consisting of four functions and S = { [x], sin^(-1) x, |x|,{x}} where , {x} denotes fractional part and [x] denotes greatest integer function , Let A, B , C are subsets of S. Suppose A : consists of odd functions (s) B : consists of discontinuous function (s) and C: consists of non-decreasing function(s) or increasing function (s). If f(x) in A nn C, g(x) in B nnC, h (x) in B" but not C and " l(x) in neither A nor B nor C . Then, answer the following. The range of g(f(x)) i

    A
    `{-1,0,1}`
    B
    `{-1,0}`
    C
    `{0,1}`
    D
    `{-2,-1,0,1}`

  • Let S denotes the set consisting of four functions and S = { [x], sin^(-1) x, |x|,{x}} where , {x} denotes fractional part and [x] denotes greatest integer function , Let A, B , C are subsets of S. Suppose A : consists of odd functions (s) B : consists of discontinuous function (s) and C: consists of non-decreasing function(s) or increasing function (s). If f(x) in A nn C, g(x) in B nnC, h (x) in B" but not C and " l(x) in neither A nor B nor C . Then, answer the following. The range of f(h(x)) is

    A
    `(0, pi/2)`
    B
    `[0, pi/2)`
    C
    `(0, pi/2]`
    D
    `[0, pi/2]`

  • The solution set for [x]{x}=1, where {x} and [x] denote fractional part and greatest integer functions, is

    A
    `R^(+)-(0,1)`
    B
    `R^(+)-{1}`
    C
    `{m+1/m:m in I-{0}}`
    D
    `{m+1/m:m in N-{1}}`

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