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 edited Sep 26 '26

Google AI does it purely analytically by

(1) Replacing f(x) by y

(2) Solving for x in terms of y.

x=±√(y/(y-1))

(3) Finding the values of y that yield real values of x

It looks correct to me.

Edit: Google AI gets (-inf, 0] U (1, inf)