NTA Abhyas JEE Main2020MathematicsFunctionsPractice

If f x = x 2 - x 2 1 + x 2 - x 2 (where . represents the greatest integer part of x ), then the range of f x is

Options

A0,1
B- 1,1
C0 , ∞
D0 , 1 2

Correct answer

D. 0 , 1 2

Step-by-step solution

x 2 - x 2 = x 2 ∴ f x = x 2 1 + x 2 = 1 + x 2 - 1 1 + x 2 = 1 - 1 1 + x 2 ∵ 0 ≤ x 2 < 1 ⇒ 1 ≤ x 2 + 1 < 2 1 2 < 1 x 2 + 1 ≤ 1 ⇒ - 1 2 > - 1 1 + x 2 ≥ - 1 1 2 > 1 + - 1 1 + x 2 ≥ 0 ⇒ Range of f x ∈ 0 , 1 2

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