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The function f : 0 ,7 → 0 , 70 where f x = x 3 - 12 x 2 + 45 x , is

Options

  1. Aone-one & onto
  2. Bmany-one & onto
  3. Cone-onto & into
  4. Dmany-one & into

Correct answer

B. many-one & onto

Step-by-step solution

f ' x = 3 x 2 - 24 x + 45 = 3 x 2 - 8 x + 15 = 3 x - 3 x - 5 ∴ f ' x changes its sign for x ∈ 0,7 ∴ f x is many-one Now f 0 = 0 ,   f 5 = 50 , f 3 = 54 ,   f 7 = 70 ∴ R a n g e ∈ 0,70 = c o - d o m a i n ∴ f x → o n t o

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