If f x = x 2 - x 2 x 2 - x 2 - 2 (where, ⋅ represents the greatest integer part of x ), then the range of f x is

Question

If f x = x 2 - x 2 x 2 - x 2 - 2 (where, ⋅ represents the greatest integer part of x ), then the range of f x is, 0 , 1, - 1 , 1, 0 , ∞, 0 , 1 3

MARKS App · Accepted Answer

We know that, x 2 - x 2 = x 2 ∴ f x = x 2 2 + x 2 = 2 + x 2 - 2 2 + x 2 = 1 - 2 2 + x 2 ∴ 0 ≤ x 2 1 ⇒ 2 ≤ x 2 + 2 3 2 3 2 x 2 + 2 ≤ 1 ⇒ - 2 3 > - 2 2 + x 2 ≥ - 1 ⇒ 1 3 > 1 + - 2 2 + x 2 ≥ 0 Hence, the range of f x is 0 , 1 3

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