Find The Values Of x graphically Which Satisfy; Function.

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Question

Find the values of x graphically which satisfy;

Function.

None of these

medium

Solution

Correct option is

Thus to find the points for which f (x) = x² – 5 is less than or equal to g(x) = [x] and g(x) = [x] is less than or equal to h(x) = x² – 2.

Where the three functions f (x), g(x) and h(x) could be plotted as;

Thus from the above graph; x² – 5 ≤ [x] ≤ x² – 2

where A and D is point of intersection of x² – 5 = ± 2 ⇒

and C is point of intersection of x² – 2 = 1

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