What is the domain of #F(x)= (x-2)/( x^3+x)#?

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Answer 1 · 2017-11-08T02:17:21

Domain: #(-oo,0)uu(0,+oo)#

#F(x)= (x-2)/(x^3+x)#

#= (x-2)/(x(x^2+1))#

#F(x)# is defined for all #x# except where #x(x^2+1) =0#

Since #(x^2+1) >=1 forall x in RR#

#-> F(x)# is defined #forall x in RR: x!=0#

Hence the domain of #F(x)# is #(-oo,0)uu(0,+oo)#

As can be deduced from the graph of #F(x)# below.

graph{(x-2)/(x^3+x) [-10, 10, -5, 5]}