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The function f : - ∞ , 1 → 0 , e 5 defined as f x = e x 3 - 3 x + 2 is

Options

  1. AMany one and onto
  2. BMany one and into
  3. COne-one and onto
  4. DOne-one and into

Correct answer

B. Many one and into

Step-by-step solution

Given, f x = e x 3 - 3 x + 2 Let, g x = x 3 - 3 x + 2 ⇒ g ′ x = 3 x 2 − 3 = 3 x 2 − 1 ⇒ g ' x ≥ 0 ,   for  x ∈ − ∞ , − 1 and g ' x ≤ 0  for  x ∈ − 1 , 1 ∴ g x is increasing as well as decreasing in different intervals ∴ f x is many-one Now, Range of f x is 0 , e 4 , but co-domain is 0 , e 5 . ∴ f x is into function

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