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Ex 1.2, 11 - Let f(x) = x4. Choose (A) f is one-one onto - Ex 1.2

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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Ex 1.2 , 11 Let f: R → R be defined as f(x) = x4. Choose the correct answer. (A) f is one-one onto (B) f is many-one onto (C) f is one-one but not onto (D) f is neither one-one nor onto f(x) = x4 Checking one-one f (x1) = (x1)4 f (x2) = (x2)4 f (x1) = f (x2) ⇒ (x1)4 = (x2)4 ⇒ x1 = x2 or x1 = –x2 Since x1 does not have unique image, It is not one-one Eg: f(–1) = (–1)4 = 1 f(1) = (1)4 = 1 Here, f(–1) = f(1) , but –1 ≠ 1 Hence, it is not one-one Check onto f(x) = x4 Let f(x) = y , such that y ∈ R x4 = y x = ± 𝑦﷮ 1﷮4﷯﷯ Note that y is a real number, it can be negative also Putting y = −3 x = ± 𝑦﷮ 1﷮4﷯﷯ 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑛𝑜𝑡 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑎𝑠 𝑟𝑜𝑜𝑡 𝑜𝑓 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑠 𝑛𝑜𝑡 𝑟𝑒𝑎𝑙 Hence, x is not real ∴ , f is not onto Hence, f is neither one-one nor onto Part D is correct

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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