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

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Answer 1 · 2018-05-10T09:09:17

Below

#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]}