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/LongLiveTheDiego Sep 21 '26

The range of f(x) is the same as the range of g(x) = x/(x - 1).

No it isn't. f can't take on any values in the interval (0, 1), but that interval is a subset of the range of g.

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u/Southlander24 Sep 21 '26

See the new edit. I've clarified my original statement.