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The function f(x)= x x^2+1 from R to R is

Options

  1. AOne-one as well as onto
  2. BOnto but not one-one
  3. CNeither one-one nor onto
  4. DOne-one but not onto

Correct answer

C. Neither one-one nor onto

Step-by-step solution

aligned & f(x)= x x^2+1 & f (x₁ )= x₁ x₁^2+1 , f (x₂ )= x₂ x₂^2+1 & f (x₁ )=f (x₂ ) aligned aligned & x₁ x₁^2+1 = x₂ x₂^2+1 & or x₁ x₂^2+x₁=x₂ x₁^2+x₂ & or x₁ x₂^2-x₂ x₁^2=x₂-x₁ & x₁ x₂=1 aligned f is neither one-one nor onto.

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