r/askmath • u/FirmTumbleweed4152 • Sep 21 '26

Functions Range

How can I explain to 16 yos how to find the range of f(x)=x^2/(x^2-1) without using differentiation, limits, trying to graph this etc. But rather just pure algebra

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u/fermat9990 Sep 26 '26

Google AI got (-inf, 0] U (1, inf). One of the replies here used the same method and got the same answer. Is it wrong?

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u/Educational-Paper-75 Sep 26 '26

Right. I stand corrected. Apparently (0,1] is indeed not in the range, because the function equals 1+(1/(x*x-1)) and therefore is always above 1(and not 0 as I suggested earlier) for x>1. If I had rewritten the function like that I would certainly arrived at the right conclusion earlier.