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

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Answer 1 · 2018-01-20T21:23:55

See explanation.

The domain is the largest subset of #RR# for which the formula is defined. Here the only values excluded from the domain are the solutions of

#x^2-1=0#

#x^2-1=0 => x^2=1 => x=-1 vv x=1#

So the domain is: #D = RR-{-1;1}#

If we look at the graph:

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

we can see that the range is #RR#

Solution: