What is the domain and range of $y = x^2 / (x^2 - 1)$ ?

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Answer 1 · 2018-05-10T09:09:17

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$y=x^2/(x^2-1)$

$y=((x^2-1)+1)/(x^2-1)$

$y=1+1/(x^2-1)$

$y=1+1/((x-1)(x+1))$

Domain: all reals except when $x=1$ and $x=-1$
Range: all reals except when $y=1$

You can verify by looking at the graph.

graph{x^2/(x^2-1) [-10, 10, -5, 5]}

What is the domain and range of y = x^2 / (x^2 - 1) y = x^2 / (x^2 - 1)?