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Let f : R --> R be a function defined a s / ( x ) = x | x |; for each x ∈ R, R being the set of real numbers. Which one of the following is correct?
  • 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
Let f: R --> R be a function defined a s / ( x ) = x | x |; for eac...
Since, f(x) = x |x| 
If f(x1) = f(x2)
or x1 | x1| = x| x2 |
or x1 = x2
So, f(x) is one-one.
Also, range of f(x) = codomain of f(x)
So, f(x) is onto.
Hence, f(x) is both one-one and onto.
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Most Upvoted Answer
Let f: R --> R be a function defined a s / ( x ) = x | x |; for eac...
Since, f(x) = x |x| 
If f(x1) = f(x2)
or x1 | x1| = x| x2 |
or x1 = x2
So, f(x) is one-one.
Also, range of f(x) = codomain of f(x)
So, f(x) is onto.
Hence, f(x) is both one-one and onto.
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Let f: R --> R be a function defined a s / ( x ) = x | x |; for each x ∈ R, R being the set of real numbers. Which one of the following is correct?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 ontoCorrect answer is option 'C'. Can you explain this answer?
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