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Let k: R\{-1} → R be given by [tex]k(x) = \frac{2x-1}{x+1}[/tex]

Prove that k is neither even nor odd.

That is strange!! But to prove it we go back to the definition;

A function, [tex]f: (-a,a) \rightarrow R[/tex] is said to be even if for all [tex]x \in (-a,a)[/tex] => [tex]f(x) = f(-x)[/tex]

And it is odd if [tex]f(x) = -f(-x)[/tex].

So: if k is even then [tex]k(-x) = k(x)[/tex] for any x

and [tex]k(x) = -k(-x)[/tex] if it is odd.

I get the feeling that my proof doesn't seem right and somewhat unimplemented... (1) is there a better way to prove and conclude that k is neither even nor odd?

And (2) if it is neither even nor odd, then what could it be?

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# Strange Function

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