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Definition of Functions

Let x [x] d...

Question

Let {x} & [x] denotes the fraction and integral part of a real number x respectively, then match the column

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Solution

$A) [x^{2}] \geq 4 x^{2} \geq 4 | x | \geq 2 x \in (- \infty, - 2] \cup [2, \infty) B) [x]^{2} - 5 [x] + 6 = 0 ([x] - 2) ([x] - 3) = 0 [x] = 2, 3 x \in [2, 4) C) x = [x] + {x} = {x} ⟹ [x] = 0 x \in [0, 1) D) [x] < - 5 x \in (- \infty, - 5)$ '

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x

[x]

denote the fractional and integral parts of a real number

x

respectively. Then a possible solution of the equation is

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Q. let {x} and [x] denote the fractional and integral part of real number x respectively. Solve 4 {x} = x + [x] . Three times the non integral solution is

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{x}

be the integer part and fractional part of a real number

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