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Questions and Answers
Which of the following statements is true about even and odd functions?
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?
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 $f(x) = x^3$?
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 $f(x) = x^4$?
What type of function is $f(x) = x^4$?
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Which of the following is not a domain in which the concepts of evenness and oddness can be defined for functions?
Which of the following is not a domain in which the concepts of evenness and oddness can be defined for functions?
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