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The continuous function f : R -->R defined by f(x) = (x+ 1)2011 is
  • a)
    Onto but not one-one
  • b)
    One-one but not onto
  • c)
     Both one-one and onto
  • d)
    Neither one-one nor onto
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The continuous function f : R -->R defined by f(x) = (x2+ 1)2011isa...
Since  therefore is not onto and f(- 1) = f(1) , therefore, f(x) is not one-one.
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Most Upvoted Answer
The continuous function f : R -->R defined by f(x) = (x2+ 1)2011isa...
R is defined as a function that takes real numbers as inputs and gives real numbers as outputs. The function is continuous, which means that there are no breaks or jumps in the graph of the function. This means that for any two real numbers a and b, if a is close to b, then f(a) is close to f(b). In other words, the function does not have any sudden changes or discontinuities.
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The continuous function f : R -->R defined by f(x) = (x2+ 1)2011isa)Onto but not one-oneb)One-one but not ontoc)Both one-one and ontod)Neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer?
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