Determine if f(x) = x + 1/x is an Even or Odd Function

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Determine if f(x) = x + 1/x is an Even or Odd Function

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I got the definitions mixed up so I was like, "im sure this function is odd, yet the test says even" ah well. Nice video

johnchristian

Df=R-{0}=R* (for every x belongs to Df, -x belongs to Df)
f(-x)=-x-1/x=-(x+1/x)=-f(x)
Therefore f is odd

nomic

Oddly enough, I ran into this function yesterday in my AoPS studies and was a bit puzzled by what they were trying to get out of it. (They ask the student to turn the equation into x^2 + 1 / x^2, but they don't say what this accomplishes.) Anyway, I'm curious if there's any reason for that—but a more general question occurred to me: do you know of any books that act as a sort of index for functions? I thought about asking you, since you do so many book reviews, but I thought the question would be kind of out-of-the-blue—but now it is not out-of-the-blue, so I'll ask :D

michaelb

I like these videos, sweet and short and makes proof reading a lot more fun

FelipeMendez

Or the leading coefficient of the variable with the greatest impact to the limit of f(x) is odd as well, therefore it is odd.

AAmado

Integrate it from -a to a then you will get to know if it is odd or even if result is 0 then odd

pranavsingh

... more generally, for all x in the domaine of f.

willyh.r.

I really love your videos. Thank you so much

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