NTA Abhyas JEE Main2020MathematicsFunctionsPractice

Let f : R → R be a function defined as f x = x 2 - 6 x 2 + 2 , then f is

Options

Aone-one but not onto
Bone-one and onto
Conto but not one-one
Dneither one-one nor onto

Correct answer

D. neither one-one nor onto

Step-by-step solution

Since, f x = f - x ∴ f is not one-one. Let, y ∈ R . Then, f x = y ⇒ y = x 2 - 6 x 2 + 2 ⇒ x 2 = 6 + 2 y 1 - y For x to be real, 6 + 2 y 1 - y ≥ 0 and 1 - y ≠ 0 ⇒ y + 3 y - 1 ≤ 0 and y ≠ 1 ⇒ - 3 ≤ y < 1 ∴ Range of f = - 3,1 ⊂ R ∴ f is not onto

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