Mastering 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 $n$

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)

Odd function (correct)

Neither even nor odd function

Even function

Both even and odd function

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