Mastering Even and Odd Functions
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Questions and Answers

Which of the following statements is true about even and odd functions?

  • Odd functions satisfy the condition $f(x) = x^n$ for odd $n$
  • Odd functions satisfy the condition $f(x) = x^n$ for even $n$
  • Even functions satisfy the condition $f(x) = x^n$ for even $n$ (correct)
  • Even functions satisfy the condition $f(x) = x^n$ for odd $n$
  • In which of the following domains can the concepts of evenness and oddness be defined for functions?

  • Only in functions whose domain and codomain both have a notion of additive inverse
  • Only in real-valued functions of a real variable
  • Only in abelian groups
  • In functions whose domain and codomain both have a notion of additive inverse, including abelian groups, all rings, all fields, and all vector spaces (correct)
  • What type of function is $f(x) = x^3$?

  • Odd function (correct)
  • Neither even nor odd function
  • Even function
  • Both even and odd function
  • What type of function is $f(x) = x^4$?

    <p>Even function</p> Signup and view all the answers

    Which of the following is not a domain in which the concepts of evenness and oddness can be defined for functions?

    <p>Non-abelian groups</p> Signup and view all the answers

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