Find The Value Of x graphically Satisfying [x] – 1 + x2 ≥ 0; Where [.] Denotes The Greatest Integer Function.

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Question

Find the value of x graphically satisfying [x] – 1 + x² ≥ 0; where [.] denotes the greatest integer function.

None of these

medium

Solution

Correct option is

As, nn [x] – 1 + x² ≥ 0

Thus to find the points for which f (x) = x² – 1 is greater than or equal tog(x) = –[x]

Where the two functions f (x) and g(x) could be plotted as:

Thus from the above graph f (x) ≥ g(x) when x Ïµ (–∞, A] ∪ [B, ∞), whereA is point of intersection of x² – 1 and –[x] when –[x] = +2

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Q6

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