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If the function f : R → R is defined by f(x) = |x|(x – sinx), then which of the following statements is TRUE?
  • a)
    f is one-one, but NOT onto
  • b)
    f is onto, but NOT one-one 
  • c)
    f is BOTH one-one and onto
  • d)
    f is NEITHER one-one NOR onto  
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the function f : R → R is defined by f(x) = |x|(x – sinx...
F(x) is a non-periodic, continuous and odd function.

Equality at x = 0  f(x) is one –one function …. (2)  
So, f(x) is both one-one & onto.
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If the function f : R → R is defined by f(x) = |x|(x – sinx...
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If the function f : R → R is defined by f(x) = |x|(x – sinx), then which of the following statements is TRUE?a)f is one-one, but NOT ontob)f is onto, but NOT one-onec)f is BOTH one-one and ontod)f is NEITHER one-one NOR onto Correct answer is option 'C'. Can you explain this answer?
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If the function f : R → R is defined by f(x) = |x|(x – sinx), then which of the following statements is TRUE?a)f is one-one, but NOT ontob)f is onto, but NOT one-onec)f is BOTH one-one and ontod)f is NEITHER one-one NOR onto Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the function f : R → R is defined by f(x) = |x|(x – sinx), then which of the following statements is TRUE?a)f is one-one, but NOT ontob)f is onto, but NOT one-onec)f is BOTH one-one and ontod)f is NEITHER one-one NOR onto Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the function f : R → R is defined by f(x) = |x|(x – sinx), then which of the following statements is TRUE?a)f is one-one, but NOT ontob)f is onto, but NOT one-onec)f is BOTH one-one and ontod)f is NEITHER one-one NOR onto Correct answer is option 'C'. Can you explain this answer?.
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