Question

If [x] ≥ –5.6, then exhaustive interval of x is (where [ ] denotes greatest integer function)


x ∈ [–5.6, ∞)


x ∈ [–5, ∞)


x ∈ (–6, ∞)


x ∈ I

Answer 1

Given :  [x] ≥ –5.6  [ ] denotes greatest integer function

To find : exhaustive interval of x

Solution:

the greatest integer function returns the largest integer

less than or equal to x. In essence, it rounds down a real number to the nearest integer.

[x] ≥ –5.6

[x]   is greatest integer function

hence only integral value comes as output

so we can very safely  say  that

=>  [x]  ≥ - 5

=> x  ∈ [–5, ∞)

for example     x  = -5.6   =>  [x]  = -6  

x  = -5.8   =>  [x]  = -6  

x  = -5.4   =>  [x]  = -6  

x  = -6   =>  [x]  = -6  

x = -5  =>  [x]  = -5      &  -5   ≥ –5.6

x  ∈ [–5, ∞)

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If u solve this UR gr8!

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