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Urmila Alex Mann
Asked: 2022-11-10T20:42:58+05:30 In:

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) = 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
Parabola
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1 Answer

  1. Correct Answer – C
    For f(x) to be real,we must have
    `(4-x^(2))/([x]+2) gt 0 and [x] + 2 ne 0`
    `rArr (4-x^(2))/([x] +2)gt 0 and x in [-2,-1)`
    CASE-I When `4-x^(2) gt 0 and [x]+ 2 ht 0`
    In this case, we have
    `x in [-2,2] and x in [-1,oo) rArr x in [-1,2]`
    Also, `x in [-2,-1)`
    `therefore ” ” x in [-1,2]`
    CASE -II When `4-x^(2) lt 0 and [x] + lt0`
    `

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