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NTA Abhyas JEE Main2020MathematicsFunctionsPractice

For a function f x = 2 x 2 + 1 x (where . denotes the greatest integer function), if 1 ≤ x < 4 , then

Options

  1. Athe range of f is 4 , 17 2
  2. Bf is bijective function
  3. Cthe maximum value of f x is 34 3
  4. Dthe minimum value of f x is 4

Correct answer

D. the minimum value of f x is 4

Step-by-step solution

We have, f x = 2 x 2 + 1 x When x ∈ 1,2 , then f x = 2 x 2 + 1 ⇒ R f = 4,10 When x ∈ 2,3 , then f x = x 2 + 1 ⇒ R f = 5,10 When x ∈ 3,4 , then f x = 2 x 2 + 1 3 ⇒ R f = 20 3 , 34 3 ∴ R f = 4 , 34 3 Clearly, for x ∈ 1,2 and x ∈ 2,3 range of f x has common elements ⇒ f x is many-one ⇒ f x is not bijective

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